{"title":"Calculus Books","description":"","products":[{"product_id":"student-solutions-manual-for-calculus-9780135732533","title":"Student Solutions Manual for Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter P Preliminaries  \u003col\u003e\n\u003cli\u003eLimits and Continuity\u003c\/li\u003e\n\u003cli\u003eDifferentiation\u003c\/li\u003e\n\u003cli\u003eTranscendental Functions\u003c\/li\u003e\n\u003cli\u003eMore Applications of Differentiation\u003c\/li\u003e\n\u003cli\u003eIntegration\u003c\/li\u003e\n\u003cli\u003eTechniques of Integration\u003c\/li\u003e\n\u003cli\u003eApplications of Integration\u003c\/li\u003e\n\u003cli\u003eConics, Parametric Curves, and Polar Curves\u003c\/li\u003e\n\u003cli\u003eSequence, Series, and Power Series\u003c\/li\u003e\n\u003cli\u003eVectors and Coordinate Geometry in 3-Space\u003c\/li\u003e\n\u003cli\u003eArc length, Metric Spaces, and Applications\u003c\/li\u003e\n\u003cli\u003eVector Functions and Curves\u003c\/li\u003e\n\u003cli\u003ePartial Differentiation\u003c\/li\u003e\n\u003cli\u003eApplications of Partial Derivatives\u003c\/li\u003e\n\u003cli\u003eMultiple Integration\u003c\/li\u003e\n\u003cli\u003eVector Fields\u003c\/li\u003e\n\u003cli\u003eVector Calculus\u003c\/li\u003e\n\u003cli\u003eDifferential Forms and Exterior Calculus\u003c\/li\u003e\n\u003cli\u003eOrdinary Differential Equations\u003c\/li\u003e\n\u003cli\u003eMore Topics in Differential Equations\u003c\/li\u003e\n\u003cli\u003eAppendix 1 Complex Numbers  Appendix 2 Complex Functions  Appendix 3 Continuous Functions  Appendix 4 The Riemann Integral  Appendix 5 Doing Calculus with Maple  Appendix 6 Doing Calculus with Python  \u003c\/li\u003e\n\u003c\/ol\u003e","brand":"Pearson Education (US)","offers":[{"title":"Default Title","offer_id":48732340650327,"sku":"9780135732533","price":19.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780135732533.jpg?v=1719996481"},{"product_id":"calculus-set-free-infinitesimals-to-the-rescue-9780192895608","title":"Calculus Set Free Infinitesimals to the Rescue","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eCalculus Set Free is a well-written and self-contained text which offers a novel and mathematically rigorous approach to the topics typically present in Calculus 1 and 2. The text is largely successful in what it sets out to accomplish, and teachers interested in offering an introduction to Calculus built on an alternative theoretical approach should consider this text. * John Ross, MAA Reviews *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eReview 1: Hyperreals, Limits, and Continuity 2: Derivatives 3: Applications of the Derivative 4: Integration 5: Transcendental Functions 6: Applications of Integration 7: Techniques of Integration 8: Alternate Representations: Parametric and Polar Curves 9: Additional Applications of Integration 10: Sequences and Series","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732613017943,"sku":"9780192895608","price":56.05,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192895608.jpg?v=1719997652"},{"product_id":"a-relatively-painless-guide-to-special-relativity-9780226821856","title":"A Relatively Painless Guide to Special Relativity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"There are myriad introductory books on special relativity. This one distinguishes itself by working through the mathematics of relativity in a very detailed yet conversational fashion. . . . Highly recommended.\" * Choice *\u003cbr\u003e“Introducing students in small, careful steps toward an understanding of the notation and physics behind special relativity has not been undertaken at this level since the text by Taylor and Wheeler from thirty years ago. Goldberg’s approach of encouraging the reader to see the simplicity behind the seemingly complex is welcome.” -- Christopher G. Tully, author of \"Elementary Particle Physics in a Nutshell\"\u003cbr\u003e“This engaging book will shape the education of a generation of physicists and astrophysicists. It defines the conceptual and mathematical stage—spacetime—on which physics is performed. From contemporary notation in the early chapters to sophisticated applications in the late chapters, Goldberg's book will not only propel students to more advanced classes, it will ease their entry into research.” -- Daniel Fabrycky, Department of Astronomy and Astrophysics, University of Chicago\u003cbr\u003e“Goldberg slings the reader straight in at the deep end . . . but with enough masterly wit to keep you afloat.” * Nature, on \"The Universe in the Rearview Mirror\" *\u003cbr\u003e“Reading this book is like taking a class with the most awesome science professor ever.” -- Annalee Newitz, founding editor of io9, on \"The Universe in the Rearview Mirror\"\u003cbr\u003e“Most physics books can’t really be described as ‘rollicking,’ but most physics books aren't written by Dave Goldberg.” -- Sean Carroll, theoretical physicist at Caltech, author of \"The Particle at the End of the Universe,\" on \"The Universe in the Rearview Mirror\"","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":48732928180567,"sku":"9780226821856","price":20.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226821856.jpg?v=1719998988"},{"product_id":"mathematical-models-in-the-biosciences-ii-9780300253696","title":"Mathematical Models in the Biosciences II","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eVolume Two of an award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Clear, enthusiastic, and communicating a love of maths, this is a useful, engaging and well-written text.”—Becca Asquith, Professor of Mathematical Immunology, Imperial College London\u003cbr\u003e\u003cbr\u003e\"This is a wonderful book, wise and witty. It would have taught me most of the math I needed for my career in research – \u003ci\u003eif\u003c\/i\u003e I did all the problems.\"—Stephen Stearns, author of \u003ci\u003eThe Evolution of Life Histories \u003c\/i\u003eand \u003ci\u003eEvolutionary Medicine\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“This well-written book covers multivariate calculus and dynamical system\u003cb\u003es\u003c\/b\u003e within the context of the biological sciences, providing well-chosen, up-to-date biomedical examples. The Markov chain, along with its many interesting applications, is also introduced.”—Hongyu He, Professor of Mathematics, Louisiana State University\u003cbr\u003e  \u003cbr\u003e\u003cbr\u003e","brand":"Yale University Press","offers":[{"title":"Default Title","offer_id":48733516628311,"sku":"9780300253696","price":35.62,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780300253696.jpg?v=1720000391"},{"product_id":"equivariant-cohomology-in-algebraic-geometry-9781009349987","title":"Equivariant Cohomology in Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This book is a much-needed introduction to a powerful and central tool in algebraic geometry and related subjects. The authors are masters of clarity and rigor. The important theorems and examples are thoroughly explained, and illuminated with well-chosen exercises. This book is an essential companion for anyone wanting to understand group actions in algebraic geometry.' Ravi Vakil, Stanford University\u003cbr\u003e'Equivariant Cohomology is a tool from algebraic topology that becomes available when groups act on spaces. In Algebraic geometry, the groups are algebraic groups, including tori, and typical spaces are toric varieties and homogeneous varieties such as Grassmannians and flag varieties. This book introduces and studies equivariant cohomology (actually equivariant Chow groups) from the perspective of algebraic geometry, beginning with the artful replacement of Borel's classifying spaces by Totaro's finite-dimensional approximations. After developing the main properties of equivariant Chow groups, including localization and GKM theory, the authors investigate equivariant Chow groups of toric varieties and flag varieties, and the equivariant classes of Schubert varieties. Reflecting the interests of the authors, special attention is paid to Schubert calculus and the links between degeneracy loci and equivariant cohomology. The text also serves as an introduction to flag varieties, their Schubert varieties, and the calculus of Schubert classes in equivariant cohomology.' Frank Sottile, Texas A\u0026amp;M University\u003cbr\u003e'Equivariant Cohomology in Algebraic Geometry by David Anderson and William Fulton offers a comprehensive, accessible exploration of the development, standard examples, and recent contributions in this fascinating field. The authors have successfully struck a balance between rigor and approachability, making it an excellent resource for young researchers in the field. The book's real strength lies in its application to toric varieties and Schubert varieties across various settings, including Grassmannians, flag varieties, degeneracy loci, and extensions to other classical types and Kac–Moody groups. The authors' treatment of Bott-Samelson desingularizations of Schubert varieties is particularly noteworthy, displaying elegance and coherence within the context of the book's material. With over 450 pages of content, Equivariant Cohomology in Algebraic Geometry offers a comprehensive resource for researchers and scholars. It is poised to become a standard reference in the field, leaving a lasting impact on the flourishing area of research for years to come.' Sara Billey, University of Washington\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Preview; 2. Defining equivariant cohomology; 3. Basic properties; 4. Grassmannians and flag varieties; 5. Localization I; 6. Conics; 7. Localization II; 8. Toric varieties; 9. Schubert calculus on Grassmannians; 10. Flag varieties and Schubert polynomials; 11. Degeneracy loci; 12. Infinite-dimensional flag varieties; 13. Symplectic flag varieties; 14. Symplectic Schubert polynomials; 15. Homogeneous varieties; 16. The algebra of divided difference operators; 17. Equivariant homology; 18. Bott–_Samelson varieties and Schubert varieties; 19. Structure constants; A. Algebraic topology; B. Specialization in equivariant Borel–_Moore homology; C. Pfaffians and Q-polynomials; D. Conventions for Schubert varieties; E. Characteristic classes and equivariant cohomology; References; Notation index; Subject index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738033566039,"sku":"9781009349987","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009349987.jpg?v=1723811694"},{"product_id":"calculus-a-complete-introduction-9781473678446","title":"Calculus A Complete Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA ''difficult'' subject so simply taught - brilliant book'' \u003c\/b\u003e- Amazon 5 star review \u003cb\u003e⭐⭐⭐⭐⭐\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e''This is a great refresher book! Lots of worked out examples, great explanations [and] hundreds of practice problems and solutions'' \u003c\/b\u003e- Amazon 5 star review \u003cb\u003e⭐⭐⭐⭐⭐\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e''This book has been very helpful for my calculus class, I recommend it to anyone that needs extra help, or just feel like learning something new.'' \u003c\/b\u003e- Amazon 5 star review \u003cb\u003e⭐⭐⭐⭐⭐\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003ci\u003eCalculus: A Complete Introduction\u003c\/i\u003e is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithm\u003c\/p\u003e","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":48739542073687,"sku":"9781473678446","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781473678446.jpg?v=1720052545"},{"product_id":"make-calculus-build-models-to-learn-visualize-and-explore-9781680457391","title":"Make: Calculus: Build models to learn, visualize,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhen Isaac Newton developed calculus in the 1600s, he was trying to tie together math and physics in an intuitive, geometrical way. But over time math and physics teaching became heavily weighted toward algebra, and less toward geometrical problem solving. However, many practicing mathematicians and physicists will get their intuition geometrically first and do the algebra later.  Make:Calculus imagines how Newton might have used 3D printed models, construction toys, programming, craft materials, and an Arduino or two to teach calculus concepts in an intuitive way. The book uses as little reliance on algebra as possible while still retaining enough to allow comparison with a traditional curriculum.  This book is not a traditional Calculus I textbook. Rather, it will take the reader on a tour of key concepts in calculus that lend themselves to hands-on projects. This book also defines terms and common symbols for them so that self-learners can learn more on their own.","brand":"O'Reilly Media","offers":[{"title":"Default Title","offer_id":48740847288663,"sku":"9781680457391","price":20.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781680457391.jpg?v=1720055814"},{"product_id":"a-course-in-calculus-and-real-analysis-9783030827410","title":"A Course in Calculus and Real Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book would be a valuable asset to a university library and that many instructors would do well to have a copy of this book in their personal libraries. In addition, I believe that some students would benefit if they possessed a copy of this book to use for reference purposes.” (Jonathan Lewin, MAA Reviews, April 15, 2019)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eNumbers and Functions.- Sequences.- Continuity and Limits.- Differentiation.- Applications of Differentiation.- Integration.- Elementary Transcendental Functions.- Applications and Approximations of Riemann Integrals.- Infinite Series and Improper Integrals.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743052312919,"sku":"9783030827410","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030827410.jpg?v=1720063901"},{"product_id":"casual-calculus-a-friendly-student-companion-volume-2-9789811241987","title":"Casual Calculus: A Friendly Student Companion -","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eYes, this is another Calculus book. However, it fits in a niche between the two predominant types of such texts.  It could be used as a textbook, albeit a streamlined one — it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide — because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes.  It is best used as a companion to a traditional text or as a refresher — with its conversational tone, its 'get right to it' content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.Exercises are structured in three sets to force multiple encounters with each topic.  Solved examples in the text are accompanied by 'You Try It' problems, which are similar to the solved examples; the students use these to see if they're ready to move forward.  Then at the end of the section, there are 'Practice Problems': more problems similar to the 'You Try It' problems, but given all at once.  Finally, each section has Challenge Problems — these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.The goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. The target audience is STEM students including those in engineering and meteorology programs.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743281131863,"sku":"9789811241987","price":52.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811241987.jpg?v=1720064904"},{"product_id":"advanced-calculus-revised-edition-9789814583930","title":"Advanced Calculus (Revised Edition)","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; Vector Spaces; Finite-Dimensional Vector Spaces; The Differential Calculus; Compactness and Completeness; Scalar Product Spaces; Differential Equations; Multilinear Functionals; Integration; Differentiable Manifolds; The Integral Calculus on Manifolds; Exterior Calculus; Potential Theory in En; Classical Mechanics.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743299645783,"sku":"9789814583930","price":32.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814583930.jpg?v=1720064989"},{"product_id":"calculus-9780135732588","title":"Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eRobert Adams\u003c\/strong\u003e is an Emeritus Professor in the Mathematics Department at the University of British Columbia. He first joined UBC in 1966 after completing a Ph.D. in Mathematics at the University of Toronto. With a keen interest in computers, mathematical typesetting, and illustration, Professor Adams became the first Canadian author in 1984 to typeset his own textbooks using TeX on a personal computer.\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eChristopher Essex\u003c\/strong\u003e is a Professor in the Department of Applied Mathematics at the University of Western Ontario, an award-winning teacher and author. Dr. Essex did pioneering work on the thermodynamics of photon and neutrino radiation.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter P Preliminaries  \u003col\u003e\n\u003cli\u003eLimits and Continuity\u003c\/li\u003e\n\u003cli\u003eDifferentiation\u003c\/li\u003e\n\u003cli\u003eTranscendental Functions\u003c\/li\u003e\n\u003cli\u003eMore Applications of Differentiation\u003c\/li\u003e\n\u003cli\u003eIntegration\u003c\/li\u003e\n\u003cli\u003eTechniques of Integration\u003c\/li\u003e\n\u003cli\u003eApplications of Integration\u003c\/li\u003e\n\u003cli\u003eConics, Parametric Curves, and Polar Curves\u003c\/li\u003e\n\u003cli\u003eSequence, Series, and Power Series\u003c\/li\u003e\n\u003cli\u003eVectors and Coordinate Geometry in 3-Space\u003c\/li\u003e\n\u003cli\u003eArc length, Metric Spaces, and Applications\u003c\/li\u003e\n\u003cli\u003eVector Functions and Curves\u003c\/li\u003e\n\u003cli\u003ePartial Differentiation\u003c\/li\u003e\n\u003cli\u003eApplications of Partial Derivatives\u003c\/li\u003e\n\u003cli\u003eMultiple Integration\u003c\/li\u003e\n\u003cli\u003eVector Fields\u003c\/li\u003e\n\u003cli\u003eVector Calculus\u003c\/li\u003e\n\u003cli\u003eDifferential Forms and Exterior Calculus\u003c\/li\u003e\n\u003cli\u003eOrdinary Differential Equations\u003c\/li\u003e\n\u003cli\u003eMore Topics in Differential Equations\u003c\/li\u003e\n\u003cli\u003eAppendix 1 Complex Numbers  Appendix 2 Complex Functions  Appendix 3 Continuous Functions  Appendix 4 The Riemann Integral  Appendix 5 Doing Calculus with Maple  Appendix 6 Doing Calculus with Python  \u003c\/li\u003e\n\u003c\/ol\u003e","brand":"Pearson Education (US)","offers":[{"title":"Default Title","offer_id":48861575119191,"sku":"9780135732588","price":56.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780135732588.jpg?v=1722247341"},{"product_id":"at-sixes-and-sevens-9780008491079","title":"At Sixes and Sevens","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn engaging, accessible introduction into how numbers work and why we shouldn't be afraid of them, frommaths expertRachel Riley.Do you know your fractions from your percentages? Your adjacent to your hypotenuse? And who really knows how to do long division, anyway?Puzzled already? Don't blame youBut fret not! You won't be At Sixes and Sevens for long. In this brilliant, well-rounded guide, Countdown''s Rachel Riley will take you back to the very basics, allow you to revisit what you learnt at school (and may have promptly forgotten, *ahem*), build your understanding of maths from the get-go and provide you with the essential toolkit to gain confidence in your numerical abilities.Discover how to divide and conquer, make your decimal debut, become a pythagoras professional and so much more with these easy-to-learn tips and tricks. Packed full of working examples, fool-proof methods, quirky trivia and brainteasers to try from puzzle-pro Dr Gareth Moore, this book is an absolute must-read for anyone and everyone who ever thought maths was above' them. Because the truth is: you can do it. What's more, it can be pretty fun too!","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863995789655,"sku":"9780008491079","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008491079.jpg?v=1722269914"},{"product_id":"the-cartoon-guide-to-calculus-9780061689093","title":"The Cartoon Guide to Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“In Gonick’s work, clever design and illustration make complicated ideas or insights strikingly clear.”\u003cbr\u003e—\u003cem\u003eNew York Times Book Review\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003eLarry Gonick, master cartoonist, former Harvard instructor, and creator of the \u003cem\u003eNew York Times\u003c\/em\u003e bestselling, Harvey Award-winning Cartoon Guide series now does for calculus what he previously did for science and history: making a complex subject comprehensible, fascinating, and fun through witty text and light-hearted graphics. Gonick’s \u003cem\u003eThe Cartoon Guide to Calculus\u003c\/em\u003e is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier \u003cem\u003eCartoon Guide to Physics\u003c\/em\u003e and \u003cem\u003eCartoon History of the Modern World\u003c\/em\u003e, will prove a boon to students, educators, and eager learners everywhere.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"How do you humanize calculus and bring its equations and concepts to life? Larry Gonick's clever and delightful answer is to have characters talking, commenting, and joking-all while rigorously teaching equations and concepts and indicating calculus's utility. It's a remarkable accomplishment-and a lot of fun.\" -- Lisa Randall, Professor of Physics, Harvard University, and author of Knocking on Heaven's Door Gonick is to graphical expositions of advanced materials as Newton or Leibniz is to calculus. The difference is that Gonick has no rival. -- Xiao-Li Meng, Whipple V. N. Jones Professor of Statistics and Department Chair, Harvard University Larry Gonick's sparkling and inventive drawings make a vivid picture out of every one of the hundreds of formulas that underlie Calculus. Even the jokers in the back row will ace the course with this book. -- David Mumford, Professor emeritus of Applied Mathematics at Brown University and recipient of the National Medal of Science I always thought that there are no magic tricks that use calculus. Larry Gonick proves me wrong. His book is correct, clear and interesting. It is filled with magical insights into this most beautiful subject. -- Persi Diaconis, Professor of Mathematics, Stanford It has no mean derivative results about the only derivatives that matter... A spunky tool-toting heroine called Delta Wye seems the perfect role model for our next generation. -- Susan Holmes, Professor of Statistics, Stanford A creative take on an old, and for many, tough subject...Gonick's cartoons and intelligent humor make it a fun read. -- Amy Langville, Recipient of the Distinguished Researcher Award at College of Charleston and South Carolina Faculty of the Year","brand":"HarperCollins Publishers Inc","offers":[{"title":"Default Title","offer_id":48864059392343,"sku":"9780061689093","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780061689093.jpg?v=1722270199"},{"product_id":"calculus-9780486404530","title":"Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eApplication-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, theorems on differentiation and antidifferentiation, the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Examples. 1967 edition. Solution guide available upon request.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864695845207,"sku":"9780486404530","price":33.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486404530.jpg?v=1722272970"},{"product_id":"elementary-calculus-9780486484525","title":"Elementary Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864737231191,"sku":"9780486484525","price":33.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"everyday-calculus-9780691157559","title":"Everyday Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. This book shows us how to see the math in our coffee, on the highway, and even in the night sky.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of American Association for the Advancement of Science's Books for General Audiences and Young Adults 2014 \"For every befuddled math student who's ever sat in class and thought, 'When am I ever going to use this?' Fernandez, assistant professor of mathematics at Wellesley College, gleefully reveals the truth: the world really does run on math... Whether describing how biology uses math to design more efficient organs and body structures or the best way to figure out when to overhaul a subway car, Fernandez keeps the tone light, as entertaining as it is informative. The book will speak most strongly to readers with some experience in trigonometry and basic calculus, but it's also accessible to those willing to put in a little extra effort. Either way, Fernandez's witty, delightful approach makes for a winning introduction to the wonderland of math behind the scenes of everyday life.\"--Publishers Weekly (starred review) \"The author earnestly and excitedly seeks to make the principles of calculus near and natural, without the intimidation of a five-pound textbook dense with equations... Fernandez invites the reader along on this work day and telegraphs an enthusiasm for seeing calculus, with hints of differential equations, presented to him. This excitement will communicate itself to the math enthusiast becoming acquainted with calculus through the author's style, which is both lively and confident.\"--Tom Schulte, MAA Reviews \"Written in a bright conversational tone, this book wonderfully integrates calculus into everyday life.\"--Devorah Bennu, GrrlScientist, The Guardian \"Professor Fernandez is a delightfully quirky writer and his book Everyday Calculus is lighthearted and compelling, connecting mathematics to daily life... Everyday Calculus will not only be found to be understandable by non-mathematicians but will also be found to be quite entertaining. Indeed, not everyone considers the calculus going on inside Tandoori ovens, and they should.\"--Robert Schaefer, New York Journal of Books \"Written in a bright conversational tone, this book wonderfully integrates calculus into everyday life.\"--GrrrlScientist \"[T]he book is perfect for a reader who really wants to know what mathematics are governing our lives and who wants to learn and understand or polish up his rusty knowledge of these mathematics.\"--A. Bultheel, European Mathematical Society \"Everyday Calculus is a triumph in the pursuit of the lofty goal of comprehending the world. Fernandez has touched upon a sensitive nerve, not just because mathematics makes most people cringe, but because the subject has allowed the passage of great things from some of the greatest minds ever to wander within the twentieth century. Oscar Fernandez is as bold as Alfred S. Posementier in his quest to deliver mathematical thinking as nature's gift to the thinking person.\"--D. Wayne Dworsky, San Francisco Book Review \"Fernandez is especially effective when linking together seemingly disparate activities for which the underlying mathematical basis is identical. As the subtitle of the book suggests, the thrust is more one of 'discovering the hidden math all around us' rather than showing 'how mathematics is used,' which provides an honest and very pleasurable journey.\"--Choice \"The book offers in clear and concise fashion much of the material found in a traditional calculus textbook, but presents it beginning with a real world observation and then developing the mathematics needed to understand the observation.\"--AAAS \"The author's style is witty, conversational and comfortable... A very captivating read.\"--Andrew Jones, Mathematics Today\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix Calculus Topics Discussed by Chapter xi CHAPTER 1 Wake Up and Smell the Functions 1 What's Trig Got to Do with Your Morning? 2 How a Rational Function Defeated Thomas Edison, and Why Induction Powers the World 5 The Logarithms Hidden in the Air 10 The Frequency of Trig Functions 14 Galileo's Parabolic Thinking 17 CHAPTER 2 Breakfast at Newton's 21 Introducing Calculus, the CNBC Way 21 Coffee Has Its Limits 25 A Multivitamin a Day Keeps the Doctor Away 30 Derivatives Are about Change 34 CHAPTER 3 Driven by Derivatives 35 Why Do We Survive Rainy Days? 36 Politics in Derivatives, or Derivatives in Politics? 39 What the Unemployment Rate Teaches Us about the Curvature of Graphs 41 America's Ballooning Population 44 Feeling Derivatives 46 The Calculus of Time Travel 47 CHAPTER 4 Connected by Calculus 51 E-Mails, Texts, Tweets, Ah! 51 The Calculus of Colds 53 What Does Sustainability Have to Do with Catching a Cold? 56 What Does Your Retirement Income Have to Do with Traffic? 58 The Calculus of the Sweet Tooth 61 CHAPTER 5 Take a Derivative and You'll Feel Better 65 I \"Heart\" Differentials 65 How Life (and Nature) Uses Calculus 67 The Costly Downside of Calculus 73 The Optimal Drive Back Home 75 Catching Speeders Efficiently with Calculus 77 CHAPTER 6 Adding Things Up, the Calculus Way 81 The Little Engine That Could ... Integrate 82 The Fundamental Theorem of Calculus 90 Using Integrals to Estimate Wait Times 93 CHAPTER 7 Derivatives Integrals: The Dream Team 97 Integration at Work-Tandoori Chicken 98 Finding the Best Seat in the House 101 Keeping the T Running with Calculus 104 Look Up to Look Back in Time 108 The Ultimate Fate of the Universe 109 The Age of the Universe 113 Epilogue 116 Appendix A Functions and Graphs 119 Appendices 1-7 125 Notes 147 Index 149","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865528545623,"sku":"9780691157559","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691157559.jpg?v=1722274405"},{"product_id":"everyday-calculus-9780691175751","title":"Everyday Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eAmerican Association for the Advancement of Science's Books for General Audiences and Young Adults One of American Association for the Advancement of Science's Books for General Audiences and Young Adults 2014 \"Fernandez's witty, delightful approach makes for a winning introduction to the wonderland of math behind the scenes of everyday life.\"--Publishers Weekly \"Written in a bright conversational tone, [Everyday Calculus] wonderfully integrates calculus into everyday life.\"--Guardian \"Fernandez is a delightfully quirky writer and his bookEveryday Calculusis lighthearted and compelling.\"--New York Journal of Books \"The author earnestly and excitedly seeks to make the principles of calculus near and natural, without the intimidation of a five-pound textbook dense with equations... Fernandez invites the reader along on this work day and telegraphs an enthusiasm for seeing calculus, with hints of differential equations, presented to him. This excitement will communicate itself to the math enthusiast becoming acquainted with calculus through the author's style, which is both lively and confident.\"--Tom Schulte, MAA Reviews \"Written in a bright conversational tone, this book wonderfully integrates calculus into everyday life.\"--GrrrlScientist \"[T]he book is perfect for a reader who really wants to know what mathematics are governing our lives and who wants to learn and understand or polish up his rusty knowledge of these mathematics.\"--A. Bultheel, European Mathematical Society \"A delightful read. [Everyday Calculus] will make you laugh and capture your imagination... [A] triumph in the pursuit of the lofty goal of comprehending the world.\"--San Francisco Book Review \"Fernandez presents a broad array of ordinary events like REM sleep, drinking coffee, commuting to work, setting aside money for retirement, catching a cold, enjoying tandoori chicken, and watching a movie... [T]hen ties each aspect to pertinent mathematics... As the subtitle of the book suggests, the thrust is more one of 'discovering the hidden math all around us' rather than showing 'how mathematics is used,' which provides an honest and very pleasurable journey.\"--Choice \"The book offers in clear and concise fashion much of the material found in a traditional calculus textbook, but presents it beginning with a real world observation and then developing the mathematics needed to understand the observation.\"--AAAS \"A very captivating read, and certainly contains something for everyone... [E]asy to drop into for individual chapters, or to read when you have a couple hours spare. [Everyday Calculus] will certainly open the eyes of any reader who wishes to appreciate the mathematics and calculus which surrounds us.\"--Mathematics Today\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix Calculus Topics Discussed by Chapter xi CHAPTER 1 Wake Up and Smell the Functions 1 What's Trig Got to Do with Your Morning? 2 How a Rational Function Defeated Thomas Edison, and Why Induction Powers the World 5 The Logarithms Hidden in the Air 10 The Frequency of Trig Functions 14 Galileo's Parabolic Thinking 17 CHAPTER 2 Breakfast at Newton's 21 Introducing Calculus, the CNBC Way 21 Coffee Has Its Limits 25 A Multivitamin a Day Keeps the Doctor Away 30 Derivatives Are about Change 34 CHAPTER 3 Driven by Derivatives 35 Why Do We Survive Rainy Days? 36 Politics in Derivatives, or Derivatives in Politics? 39 What the Unemployment Rate Teaches Us about the Curvature of Graphs 41 America's Ballooning Population 44 Feeling Derivatives 46 The Calculus of Time Travel 47 CHAPTER 4 Connected by Calculus 51 E-Mails, Texts, Tweets, Ah! 51 The Calculus of Colds 53 What Does Sustainability Have to Do with Catching a Cold? 56 What Does Your Retirement Income Have to Do with Traffic? 58 The Calculus of the Sweet Tooth 61 CHAPTER 5 Take a Derivative and You'll Feel Better 65 I \"Heart\" Differentials 65 How Life (and Nature) Uses Calculus 67 The Costly Downside of Calculus 73 The Optimal Drive Back Home 75 Catching Speeders Efficiently with Calculus 77 CHAPTER 6 Adding Things Up, the Calculus Way 81 The Little Engine That Could ... Integrate 82 The Fundamental Theorem of Calculus 90 Using Integrals to Estimate Wait Times 93 CHAPTER 7 Derivatives Integrals: The Dream Team 97 Integration at Work-Tandoori Chicken 98 Finding the Best Seat in the House 101 Keeping the T Running with Calculus 104 Look Up to Look Back in Time 108 The Ultimate Fate of the Universe 109 The Age of the Universe 113 Epilogue 116 Appendix A Functions and Graphs 119 Appendices 1-7 125 Notes 147 Index 149","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537130839,"sku":"9780691175751","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175751.jpg?v=1722274447"},{"product_id":"visual-differential-geometry-and-forms-9780691203706","title":"Visual Differential Geometry and Forms","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Finalist for the PROSE Award in Mathematics, Association of American Publishers\"\u003cbr\u003e\"Needham proposes to provide a truly geometric 'visual' explication of differential geometry, and he succeeds brilliantly. I know nothing like it in the literature.\"\u003cb\u003e---Frank Morgan, \u003ci\u003eEMS Magazine\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[The] book offers a truly unique and original take on differential geometry, and it amply deserves inclusion within the pantheon of textbook deities.\"\u003cb\u003e---Eric Poisson, \u003ci\u003eNotices of the AMS\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This is a valuable and beautifully created guide to what can at first seem a confusing area of mathematical physics. There are other contenders that try to teach this subject, but this is the best that I have come across so far and I will continue to enjoy learning from it (and almost certainly teaching from it) over the coming years, I am sure.\"\u003cb\u003e---Jonathan Shock, \u003ci\u003eMathemafrica\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[Proactively] rethinks the way this important area of mathematics should be considered and taught.\" * MathSciNet *\u003cbr\u003e\"The book is a remarkable and highly original approach to the basic stem of differential geometry. And that mathematical trunk has roots and branches in so many other unexpected yet related subjects, each of which can be equally well approached from the same geometrical point of view.\"\u003cb\u003e---Adhemar Bultheel, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[\u003ci\u003eVisual Differential Geometry and Forms\u003c\/i\u003e] its peers. It is fun to read and provides a unique and intuitive approach to differential geometry. The author’s passion for the subject is evident throughout the book. Although Needham’s approach is unorthodox, it is rewarding, and complements the exposition found in standard textbooks.\"\u003cb\u003e---Sean M. Eli \u0026amp; Krešmir Josić, \u003ci\u003eSIAM Review\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865546142039,"sku":"9780691203706","price":35.7,"currency_code":"GBP","in_stock":true}]},{"product_id":"calculus-reordered-9780691218786","title":"Calculus Reordered","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865550434647,"sku":"9780691218786","price":17.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691218786.jpg?v=1722274516"},{"product_id":"calculus-9781319050733","title":"Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Macmillan Learning","offers":[{"title":"Default Title","offer_id":48866555756887,"sku":"9781319050733","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781319050733.jpg?v=1722279201"},{"product_id":"vector-calculus-9781429215084","title":"Vector Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Macmillan Learning","offers":[{"title":"Default Title","offer_id":48867039281495,"sku":"9781429215084","price":65.54,"currency_code":"GBP","in_stock":true}]},{"product_id":"infinite-powers-the-story-of-calculus-the-language-of-the-universe-9781786492975","title":"Infinite Powers: The Story of Calculus - The","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eShortlisted for the Royal Society Science Book Prize 2019\u003c\/b\u003e\u003cb\u003e\u003cbr\u003e\u003cbr\u003eA magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eThis is the captivating story of mathematics' greatest ever idea: \u003ci\u003ecalculus. \u003c\/i\u003eWithout it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. \u003cbr\u003e\u003cbr\u003eTaking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence. Filled with idiosyncratic characters from Pythagoras to Fourier, \u003ci\u003eInfinite Powers\u003c\/i\u003e is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eWarning: this book is dangerous. It will make you love mathematics. Even more, there is a nonzero risk it will turn you into a mathematician.\u003c\/b\u003e * Nassim Nicholas Taleb, bestselling author of The Black Swan *\u003cbr\u003e\u003cb\u003eFascinating \u003c\/b\u003ereading. * Scientific American *\u003cbr\u003e\u003cb\u003eEloquent, erudite and charming. A remarkable story. Strogatz is a world class mathematician and a world class science writer. With a light touch and razor-sharp clarity, he tells the remarkable story of a mathematical breakthrough that changed the world - and continues to do so.\u003c\/b\u003e * Alex Bellos, bestselling author of Alex's Adventures in Numberland *\u003cbr\u003e\u003cb\u003eGlorious! A master class in accessible maths writing and a perfect read for anyone who feels like they never quite understood what all the fuss was about. It had me leaping for joy.\u003c\/b\u003e * Hannah Fry, bestselling author of Hello World and presenter of BBC R4’s The Curious Cases of Rutherford and Fry *\u003cbr\u003e\u003cb\u003eSimple, lucid, amusing, informative, and a pleasure to read. If you want to know where calculus came from, how it works, what it's good for, and where it's going next, this is the book for you.\u003c\/b\u003e * Professor Ian Stewart, author of Significant Figures *\u003cbr\u003eA \u003cb\u003efine\u003c\/b\u003e, \u003cb\u003ethoughtful \u003c\/b\u003eattempt to make the greatest stories relating to calculus accessible... After reading \u003ci\u003eInfinite Powers\u003c\/i\u003e, we should no longer fear calculus. * Literary Review *\u003cbr\u003e\u003cb\u003eThe most fascinating book I have ever read. If you have even the slightest curiosity about maths and its role in this world, I implore you to read this amazing book.\u003c\/b\u003e * Jo Boaler, professor of mathematics education, Stanford University *\u003cbr\u003e\u003cb\u003eA wide-ranging, humane, thoroughly readable take on one of the greatest ideas our species has ever produced.\u003c\/b\u003e * Jordan Ellenberg, author of How Not to Be Wrong *\u003cbr\u003eFascinating anecdotes abound in \u003ci\u003eInfinite Powers\u003c\/i\u003e... [Strogatz] has written \u003cb\u003ea romp through the history of calculus.\u003c\/b\u003e * Nature *\u003cbr\u003e\u003cb\u003eA tour de force. Elegant and ebullient. Strogatz speaks to everyone, reminding us why mathematics matters in a practical sense while all the time highlighting its beauty.\u003c\/b\u003e * Lisa Randall, Professor of Physics at Harvard University and author of Dark Matter and The Dinosaurs *\u003cbr\u003e\u003cb\u003eA highly readable account of calculus and its modern applications - all done with the human touch.\u003c\/b\u003e * Dr David Acheson, Emeritus Fellow, Oxford University and author of The Calculus Story *\u003cbr\u003e\u003cb\u003eAn incalculable pleasure. If calculus is the language of the universe, then Steven Strogatz is its Homer.\u003c\/b\u003e * Daniel Gilbert, author of Stumbling on Happiness *\u003cbr\u003e\u003cb\u003eIn this engaging book, Steven Strogatz illuminates the importance of calculus and explains its mysteries as only he can.\u003c\/b\u003e * Sean Carroll, author of The Particle at the End of the Universe *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Infinity 2: The Man Who Harnessed Infinity 3: Discovering the Laws of Motion 4: The Dawn of Differential Calculus 5: The Crossroads 6: The Vocabulary of Change 7: The Secret Fountain 8: Fictions of the Mind 9: The Logical Universe 10: Making Waves 11: The Future of Calculus","brand":"Atlantic Books","offers":[{"title":"Default Title","offer_id":48868368810327,"sku":"9781786492975","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781786492975.jpg?v=1722287712"},{"product_id":"change-is-the-only-constant-9780316509084","title":"Change Is the Only Constant","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBy spinning 28 engaging mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day - love, risk, time and, most importantly, change. Divided into two parts, Moments and Eternities, and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, \u003ci\u003eChange is the Only Constant\u003c\/i\u003e unearths connections between calculus, art, literature and a beloved dog named Elvis. This is not just maths for maths'' sake; it''s maths for the sake of becoming a wiser and more thoughtful human.","brand":"Black Dog \u0026 Leventhal Publishers Inc","offers":[{"title":"Default Title","offer_id":48883971293527,"sku":"9780316509084","price":20.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780316509084.jpg?v=1722529842"},{"product_id":"applied-calculus-9780357723487","title":"Applied Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDiscover the relevance of mathematics in your own life as you master important concepts and skills in Waner\/Costenoble's APPLIED CALCULUS, 8th Edition. Updated, numerous examples and applications use real data from well-known businesses, current economic and life events -- from cryptocurrency to COVID -- to demonstrate how the principles you are learning impact you. Readable, streamlined content clearly presents concepts while numerous learning features and tools help you review and practice. Spreadsheet and TI graphing calculator instructions appear where needed. In addition, WebAssign online tools and an interactive eTextbook include teaching videos by an award-winning instructor. You can refine your skills in the necessary math prerequisites with additional examples and powerful adaptive practice sessions. A helpful website from the authors also offers online tutorials and videos on every topic to support your learning, no matter what your learning style.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e0. PRECALCULUS REVIEW. Real Numbers. Exponents and Radicals. Using Exponent Identities Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. The Coordinate Plane. Logarithms. 1. FUNCTIONS AND APPLICATIONS. Functions from the Numerical, Algebraic, and Graphical Viewpoints. Functions and Models. Linear Functions and Models. Linear Regression. 2. NONLINEAR FUNCTIONS AND MODELS. Quadratic Functions and Models. Exponential Functions and Models. The Number e and Exponential Growth and Decay. Logistic and Logarithmic Functions and Models.. 3. INTRODUCTION TO THE DERIVATIVE. Limits: Numerical and GraphicalViewpoints. Limits and Continuity. Limits: Algebraic Viewpoint. Average Rate of Change. Derivatives: Numerical and Graphical Viewpoints. Derivatives: Algebraic Viewpoint. 4. TECHNIQUES OF DIFFERENTIATION. Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. 5. APPLICATIONS OF THE DERIVATIVE. Maxima and Minima. Applications of Maxima and Minima. Higher Order Derivatives: Acceleration and Concavity. Analyzing Graphs. Related Rates. Elasticity. 6. THE INTEGRAL. The Indefinite Integral. Substitution. The Definite Integral. The Fundamental Theorem of Calculus. 7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Integration by Parts. Area Between Two Curves. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications. 8. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications. 9. TRIGONOMETRIC MODELS. Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications.","brand":"Book Curl","offers":[{"title":"Default Title","offer_id":48884054786391,"sku":"9780357723487","price":76.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780357723487.jpg?v=1722530228"},{"product_id":"calculus-equations-answers-9781423208563","title":"Calculus Equations  Answers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFor every student who has ever found the answer to a particular calculus equation elusive or a certain theorem impossible to remember, QuickStudy comes to the rescue! This 3-panel (6-page) comprehensive guide offers clear and concise examples, detailed explanations and colorful graphsaall guaranteed to make calculus a breeze! Easy-to-use icons help students go right to the equations and problems they need to learn, and call out helpful tips to use and common pitfalls to avoid.","brand":"Barcharts, Inc","offers":[{"title":"Default Title","offer_id":48885584298327,"sku":"9781423208563","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781423208563.jpg?v=1722536993"},{"product_id":"variational-calculus-on-time-scales-9781536143232","title":"Variational Calculus on Time Scales","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book encompasses recent developments of variational calculus for time scales. It is intended for use in the field of variational calculus and dynamic calculus for time scales. It is also suitable for graduate courses in the above fields. This book contains eight chapters, and these chapters are pedagogically organized. This book is specially designed for those who wish to understand variational calculus on time scales without having extensive mathematical background.The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text material of this book is presented in a highly readable and mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886101705047,"sku":"9781536143232","price":195.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781536143232.jpg?v=1722538822"},{"product_id":"mathematics-for-agricultural-and-life-sciences-principles-of-calculus-with-solved-problems-9781536180275","title":"Mathematics for Agricultural and Life Sciences:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne of the difficulties that arise in teaching mathematics is related to the identification of the target and the most appropriate teaching methods for the people who are part of it. This aspect, true for all disciplines, applies to mathematics in particular. In fact, for example, an axiomatic approach is certainly suitable for Mathematical, Physical and Engineering Sciences, while students of many applied sciences, such as Agricultural and Life Sciences, need to focus on calculation tools and methodologies useful for their professional development rather than in dealing with the theoretical foundations of mathematics. The peculiarity of this book is not so much in setting classical approach \"Theorem: Hypothesis, Thesis\" with relative proofs, but in adopting a more pragmatic approach that renounce classical demonstrations, while maintaining a formal coherence in the topics dealt with. In this perspective, considering the approach required by the target to which it is addressed, the objective of this book is to provide methods to studying the variation of a phenomenon and its cumulative effects and consequently the study of the functions and the calculation of integrals respectively. One of the qualifying features is given by a series of completely resolved problems, occupying two-thirds of the volume, in which each mathematical step is detailed to understand \"step by step\" how to obtain the solution.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Principles of Set Theory; Real Numbers; Functions of Real Variables; Limit of a Function; Derivative of a Function; Study of a Function: Points of Maximum and Minimum, Points of Inflection; Indefinite Integral; Definite Integral; Calculation of Function Limits; Calculation of Function Derivatives; Problems Related to the Study of Functions; Calculation of Integrals; Index.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886174122327,"sku":"9781536180275","price":163.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781536180275.jpg?v=1722539086"},{"product_id":"foundations-of-iso-differential-calculus-volume-6-theory-of-iso-functions-of-a-real-iso-variable-9781634850216","title":"Foundations of Iso-Differential Calculus: Volume","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is intended for readers who have had a course in theory of functions, isodifferential calculus and it can also be used for a senior undergraduate course. Chapter One deals with the infinite sets. We introduce the main operations on the sets. They are considered as the one-to-one correspondences, the denumerable sets and the nondenumerable sets, and their properties. Chapter Two introduces the point sets. They are defined as the limit points, the interior points, the open sets, and the closed sets. Also included are the structure of the bounded open and the closed sets, and an examination of some of their main properties. Chapter Three describes the measurable sets. They are defined and deducted as the main properties of the measure of a bounded open set, a bounded closed set, and the outer and the inner measures of a bounded set. Chapter Four is devoted to the theory of the measurable iso-functions. They are defined as the main classes of the measurable iso-functions and their associated properties are defined as well. In Chapter Five, the Lebesgue iso-integral of a bounded iso-function continue the discussion of the book. Their main properties are given. In Chapter Six the square iso-summable iso-functions, the iso-orthogonal systems, the iso-spaces Lp and l p, p \u0026gt; 1 are studied. The Stieltjes iso-integral and its properties are investigated in Chapter Seven.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48887236100439,"sku":"9781634850216","price":170.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781634850216.jpg?v=1722543625"},{"product_id":"foundations-of-iso-differential-calculus-volume-i-9781685074777","title":"Foundations of Iso-Differential Calculus: Volume","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the second edition of Foundations of Iso-Differential Calculus, Volume 1, which gives an overview of the development of iso-differential calculus. The second edition introduces a new class of iso-functions, named iso-functions of the fifth kind. Also, further examples, exercises and problems have been added. Chapter 1 reviews Ruggero Maria Santilli''s scientific journey, identifying its most important references. Chapter 2 introduces iso-real numbers, some basic functions and their properties. Chapter 3 defines sequences of iso-real numbers and deduces their properties. Chapter 4 gives definitions for five kinds of iso-functions and outlines their properties. Chapter 5 introduces the limits of iso-functions and continuous iso-functions. Chapter 6 presents the first comprehensive study of iso-differential calculus for the specific intent of showing its non-triviality. Chapter 7 reflects integral calculus in the language of iso-mathematics. Lastly, Chapter 8 outlines the isodual iso-mathematics and presents the first comprehensive study of isodual iso-differential calculus.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48887495754071,"sku":"9781685074777","price":163.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781685074777.jpg?v=1722544843"},{"product_id":"computational-calculus-9783031296604","title":"Computational Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book offers readers the methods that are necessary to apply the power of calculus to analyze real problems.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084755706199,"sku":"9783031296604","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031296604.jpg?v=1725553237"},{"product_id":"calculus-of-variations-and-optimal-control-theory-a-concise-introduction-9780691151878","title":"Calculus of Variations and Optimal Control Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOffers an introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. This book traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Each chapter ends with a rich and useful section of notes and references. The exercises are merely problems or even theorems. The author of the book presents a large list of references and a detailed index of notions, names, and symbols. The graphical presentation of the book is pleasant... [T]his book is well written, it fully deserves all its goals mentioned at the beginning of the review, and is a pleasure to read it.\"--Marian Muresan, Mathematica \"This is an extremely well-crafted textbook. If you plan to teach a first course to advanced students on the calculus of variations and optimal control and you like the selection of topics that the author has chosen to present (and I do), it is the text you need. What impresses me most is the careful balance between the formal derivations and the explanations that precede or accompany the statements and proofs... All in all, it is a first-rate, enjoyable text.\"--Zvi Artstein, Mathematical Reviews Clippings","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49371743748439,"sku":"9780691151878","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"calculus-ii-sparkcharts-9781411470224","title":"Calculus II Sparkcharts","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Spark","offers":[{"title":"Default Title","offer_id":49371885011287,"sku":"9781411470224","price":8.2,"currency_code":"GBP","in_stock":true}]},{"product_id":"gold-c1-advanced-new-edition-students-etext-access-card-9781292202051","title":"Gold C1 Advanced New Edition Students eText","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Pearson Education Limited","offers":[{"title":"Default Title","offer_id":49396214956375,"sku":"9781292202051","price":42.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292202051.jpg?v=1730415126"},{"product_id":"a-relatively-painless-guide-to-special-relativity-9780226825427","title":"A Relatively Painless Guide to Special Relativity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"There are myriad introductory books on special relativity. This one distinguishes itself by working through the mathematics of relativity in a very detailed yet conversational fashion. . . . Highly recommended.\" * Choice *\u003cbr\u003e“Introducing students in small, careful steps toward an understanding of the notation and physics behind special relativity has not been undertaken at this level since the text by Taylor and Wheeler from thirty years ago. Goldberg’s approach of encouraging the reader to see the simplicity behind the seemingly complex is welcome.” -- Christopher G. Tully, author of \"Elementary Particle Physics in a Nutshell\"\u003cbr\u003e“This engaging book will shape the education of a generation of physicists and astrophysicists. It defines the conceptual and mathematical stage—spacetime—on which physics is performed. From contemporary notation in the early chapters to sophisticated applications in the late chapters, Goldberg's book will not only propel students to more advanced classes, it will ease their entry into research.” -- Daniel Fabrycky, Department of Astronomy and Astrophysics, University of Chicago\u003cbr\u003e“Goldberg slings the reader straight in at the deep end . . . but with enough masterly wit to keep you afloat.” * Nature, on \"The Universe in the Rearview Mirror\" *\u003cbr\u003e“Reading this book is like taking a class with the most awesome science professor ever.” -- Annalee Newitz, founding editor of io9, on \"The Universe in the Rearview Mirror\"\u003cbr\u003e“Most physics books can’t really be described as ‘rollicking,’ but most physics books aren't written by Dave Goldberg.” -- Sean Carroll, theoretical physicist at Caltech, author of \"The Particle at the End of the Universe,\" on \"The Universe in the Rearview Mirror\"","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":49400133419351,"sku":"9780226825427","price":76.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226825427.jpg?v=1730469837"},{"product_id":"infinite-powers-9780358299288","title":"Infinite Powers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Mariner Books","offers":[{"title":"Default Title","offer_id":49401866486103,"sku":"9780358299288","price":14.41,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780358299288.jpg?v=1730478735"},{"product_id":"div-grad-curl-and-all-that-9780393925166","title":"Div Grad Curl and All That","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis new fourth edition of the acclaimed and bestselling \u003cem\u003eDiv, Grad, Curl, and All That\u003c\/em\u003e has been carefully revised and now includes updated notations and seven new example exercises.","brand":"WW Norton \u0026 Co","offers":[{"title":"Default Title","offer_id":49402031964503,"sku":"9780393925166","price":42.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780393925166.jpg?v=1730479198"},{"product_id":"calculus-one-variable-10e-chapters-1-12-student-solutions-manual-9780470105535","title":"Calculus One Variable 10e Chapters 1  12 Student","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePractice calculus with this solutions manual\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFor students using \u003ci\u003eCalculus: One and Several Variables\u003c\/i\u003e for classroom instruction, this complete solutions manual for chapters 1-12 provides the answer key to the one-variable problems presented in the text. Now in its tenth edition, \u003ci\u003eCalculus: One and Several Variables\u003c\/i\u003e has become known for its easy-to-understand writing style and balance of theory and application. With this solutions manual, students can apply their knowledge using the problems presented in the first 12 chapters and check their work as they go.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eCHAPTER 1 1\u003c\/p\u003e \u003cp\u003eCHAPTER 2 20\u003c\/p\u003e \u003cp\u003eCHAPTER 3 37\u003c\/p\u003e \u003cp\u003eCHAPTER 4 63\u003c\/p\u003e \u003cp\u003eCHAPTER 5 125\u003c\/p\u003e \u003cp\u003eCHAPTER 6 157\u003c\/p\u003e \u003cp\u003eCHAPTER 7 186\u003c\/p\u003e \u003cp\u003eCHAPTER 8 220\u003c\/p\u003e \u003cp\u003eCHAPTER 9 263\u003c\/p\u003e \u003cp\u003eCHAPTER 10 288\u003c\/p\u003e \u003cp\u003eCHAPTER 11 322\u003c\/p\u003e \u003cp\u003eCHAPTER 12 346\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402286866775,"sku":"9780470105535","price":52.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470105535.jpg?v=1730479952"},{"product_id":"applications-in-statistics-2e-360-wiley-series-in-probability-and-statistics-9780471391043","title":"Applications in Statistics 2e 360 Wiley Series in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDesigned to help motivate the learning of advanced calculus by demonstrating its relevance in the field of statistics, this successful text features detailed coverage of optimization techniques and their applications in statistics while introducing the reader to approximation theory. The \u003ci\u003eSecond Edition\u003c\/i\u003e provides substantial new coverage of the material, including three new chapters and a large appendix that contains solutions to almost all of the exercises in the book. Applications of some of these methods in statistics are discusses.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This is an exceptional book, which I would recommend for anyone beginning a career in statistical research.\" (\u003ci\u003eJournal of the American Statistical Association\u003c\/i\u003e, September 2004)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003ePreface to the First Edition xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. An Introduction to Set Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. The Concept of a Set 1\u003c\/p\u003e \u003cp\u003e1.2. Set Operations 2\u003c\/p\u003e \u003cp\u003e1.3. Relations and Functions 4\u003c\/p\u003e \u003cp\u003e1.4. Finite Countable and Uncountable Sets 6\u003c\/p\u003e \u003cp\u003e1.5. Bounded Sets 9\u003c\/p\u003e \u003cp\u003e1.6. Some Basic Topological Concepts 10\u003c\/p\u003e \u003cp\u003e1.7. Examples in Probability and Statistics 13\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 15\u003c\/p\u003e \u003cp\u003eExercises 17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Basic Concepts in Linear Algebra 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Vector Spaces and Subspaces 21\u003c\/p\u003e \u003cp\u003e2.2. Linear Transformations 25\u003c\/p\u003e \u003cp\u003e2.3. Matrices and Determinants 27\u003c\/p\u003e \u003cp\u003e2.3.1. Basic Operations on Matrices 28\u003c\/p\u003e \u003cp\u003e2.3.2. The Rank of a Matrix 33\u003c\/p\u003e \u003cp\u003e2.3.3. The Inverse of a Matrix 34\u003c\/p\u003e \u003cp\u003e2.3.4. Generalized Inverse of a Matrix 36\u003c\/p\u003e \u003cp\u003e2.3.5. Eigenvalues and Eigenvectors of a Matrix 36\u003c\/p\u003e \u003cp\u003e2.3.6. Some Special Matrices 38\u003c\/p\u003e \u003cp\u003e2.3.7. The Diagonalization of a Matrix 38\u003c\/p\u003e \u003cp\u003e2.3.8. Quadratic Forms 39\u003c\/p\u003e \u003cp\u003e2.3.9. The Simultaneous Diagonalization of Matrices 40\u003c\/p\u003e \u003cp\u003e2.3.10. Bounds on Eigenvalues 41\u003c\/p\u003e \u003cp\u003e2.4. Applications of Matrices in Statistics 43\u003c\/p\u003e \u003cp\u003e2.4.1. The Analysis of the Balanced Mixed Model 43\u003c\/p\u003e \u003cp\u003e2.4.2. The Singular-Value Decomposition 45\u003c\/p\u003e \u003cp\u003e2.4.3. Extrema of Quadratic Forms 48\u003c\/p\u003e \u003cp\u003e2.4.4. The Parameterization of Orthogonal Matrices 49\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 50\u003c\/p\u003e \u003cp\u003eExercises 53\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Limits and Continuity of Functions 57\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Limits of a Function 57\u003c\/p\u003e \u003cp\u003e3.2. Some Properties Associated with Limits of Functions 63\u003c\/p\u003e \u003cp\u003e3.3. The o O Notation 65\u003c\/p\u003e \u003cp\u003e3.4. Continuous Functions 66\u003c\/p\u003e \u003cp\u003e3.4.1. Some Properties of Continuous Functions 71\u003c\/p\u003e \u003cp\u003e3.4.2. Lipschitz Continuous Functions 75\u003c\/p\u003e \u003cp\u003e3.5. Inverse Functions 76\u003c\/p\u003e \u003cp\u003e3.6. Convex Functions 79\u003c\/p\u003e \u003cp\u003e3.7. Continuous and Convex Functions in Statistics 82\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 87\u003c\/p\u003e \u003cp\u003eExercises 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Differentiation 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. The Derivative of a Function 93\u003c\/p\u003e \u003cp\u003e4.2. The Mean Value Theorem 99\u003c\/p\u003e \u003cp\u003e4.3. Taylor’s Theorem 108\u003c\/p\u003e \u003cp\u003e4.4. Maxima and Minima of a Function 112\u003c\/p\u003e \u003cp\u003e4.4.1. A Sufficient Condition for a Local Optimum 114\u003c\/p\u003e \u003cp\u003e4.5. Applications in Statistics 115\u003c\/p\u003e \u003cp\u003e4.5.1. Functions of Random Variables 116\u003c\/p\u003e \u003cp\u003e4.5.2. Approximating Response Functions 121\u003c\/p\u003e \u003cp\u003e4.5.3. The Poisson Process 122\u003c\/p\u003e \u003cp\u003e4.5.4. Minimizing the Sum of Absolute Deviations 124\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 125\u003c\/p\u003e \u003cp\u003eExercises 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Infinite Sequences and Series 132\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Infinite Sequences 132\u003c\/p\u003e \u003cp\u003e5.1.1. The Cauchy Criterion 137\u003c\/p\u003e \u003cp\u003e5.2. Infinite Series 140\u003c\/p\u003e \u003cp\u003e5.2.1. Tests of Convergence for Series of Positive Terms 144\u003c\/p\u003e \u003cp\u003e5.2.2. Series of Positive and Negative Terms 158\u003c\/p\u003e \u003cp\u003e5.2.3. Rearrangement of Series 159\u003c\/p\u003e \u003cp\u003e5.2.4. Multiplication of Series 162\u003c\/p\u003e \u003cp\u003e5.3. Sequences and Series of Functions 165\u003c\/p\u003e \u003cp\u003e5.3.1. Properties of Uniformly Convergent Sequences and Series 169\u003c\/p\u003e \u003cp\u003e5.4. Power Series 174\u003c\/p\u003e \u003cp\u003e5.5. Sequences and Series of Matrices 178\u003c\/p\u003e \u003cp\u003e5.6. Applications in Statistics 182\u003c\/p\u003e \u003cp\u003e5.6.1. Moments of a Discrete Distribution 182\u003c\/p\u003e \u003cp\u003e5.6.2. Moment and Probability Generating Functions 186\u003c\/p\u003e \u003cp\u003e5.6.3. Some Limit Theorems 191\u003c\/p\u003e \u003cp\u003e5.6.3.1. The Weak Law of Large Numbers ŽKhinchine’s Theorem. 192\u003c\/p\u003e \u003cp\u003e5.6.3.2. The Strong Law of Large Numbers ŽKolmogorov’s Theorem. 192\u003c\/p\u003e \u003cp\u003e5.6.3.3. The Continuity Theorem for Probability Generating Functions 192\u003c\/p\u003e \u003cp\u003e5.6.4. Power Series and Logarithmic Series Distributions 193\u003c\/p\u003e \u003cp\u003e5.6.5. Poisson Approximation to Power Series Distributions 194\u003c\/p\u003e \u003cp\u003e5.6.6. A Ridge Regression Application 195\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 197\u003c\/p\u003e \u003cp\u003eExercises 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Integration 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. Some Basic Definitions 205\u003c\/p\u003e \u003cp\u003e6.2. The Existence of the Riemann Integral 206\u003c\/p\u003e \u003cp\u003e6.3. Some Classes of Functions That Are Riemann Integrable 210\u003c\/p\u003e \u003cp\u003e6.3.1. Functions of Bounded Variation 212\u003c\/p\u003e \u003cp\u003e6.4. Properties of the Riemann Integral 215\u003c\/p\u003e \u003cp\u003e6.4.1. Change of Variables in Riemann Integration 219\u003c\/p\u003e \u003cp\u003e6.5. Improper Riemann Integrals 220\u003c\/p\u003e \u003cp\u003e6.5.1. Improper Riemann Integrals of the Second Kind 225\u003c\/p\u003e \u003cp\u003e6.6. Convergence of a Sequence of Riemann Integrals 227\u003c\/p\u003e \u003cp\u003e6.7. Some Fundamental Inequalities 229\u003c\/p\u003e \u003cp\u003e6.7.1. The Cauchy_Schwarz Inequality 229\u003c\/p\u003e \u003cp\u003e6.7.2. H¨older’s Inequality 230\u003c\/p\u003e \u003cp\u003e6.7.3. Minkowski’s Inequality 232\u003c\/p\u003e \u003cp\u003e6.7.4. Jensen’s Inequality 233\u003c\/p\u003e \u003cp\u003e6.8. Riemann_Stieltjes Integral 234\u003c\/p\u003e \u003cp\u003e6.9. Applications in Statistics 239\u003c\/p\u003e \u003cp\u003e6.9.1. The Existence of the First Negative Moment of a Continuous Distribution 242\u003c\/p\u003e \u003cp\u003e6.9.2. Transformation of Continuous Random Variables 246\u003c\/p\u003e \u003cp\u003e6.9.3. The Riemann_Stieltjes Representation of the Expected Value 249\u003c\/p\u003e \u003cp\u003e6.9.4. Chebyshev’s Inequality 251\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 252\u003c\/p\u003e \u003cp\u003eExercises 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Multidimensional Calculus 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. Some Basic Definitions 261\u003c\/p\u003e \u003cp\u003e7.2. Limits of a Multivariable Function 262\u003c\/p\u003e \u003cp\u003e7.3. Continuity of a Multivariable Function 264\u003c\/p\u003e \u003cp\u003e7.4. Derivatives of a Multivariable Function 267\u003c\/p\u003e \u003cp\u003e7.4.1. The Total Derivative 270\u003c\/p\u003e \u003cp\u003e7.4.2. Directional Derivatives 273\u003c\/p\u003e \u003cp\u003e7.4.3. Differentiation of Composite Functions 276\u003c\/p\u003e \u003cp\u003e7.5. Taylor’s Theorem for a Multivariable Function 277\u003c\/p\u003e \u003cp\u003e7.6. Inverse and Implicit Function Theorems 280\u003c\/p\u003e \u003cp\u003e7.7. Optima of a Multivariable Function 283\u003c\/p\u003e \u003cp\u003e7.8. The Method of Lagrange Multipliers 288\u003c\/p\u003e \u003cp\u003e7.9. The Riemann Integral of a Multivariable Function 293\u003c\/p\u003e \u003cp\u003e7.9.1. The Riemann Integral on Cells 294\u003c\/p\u003e \u003cp\u003e7.9.2. Iterated Riemann Integrals on Cells 295\u003c\/p\u003e \u003cp\u003e7.9.3. Integration over General Sets 297\u003c\/p\u003e \u003cp\u003e7.9.4. Change of Variables in n-Tuple Riemann Integrals 299\u003c\/p\u003e \u003cp\u003e7.10. Differentiation under the Integral Sign 301\u003c\/p\u003e \u003cp\u003e7.11. Applications in Statistics 304\u003c\/p\u003e \u003cp\u003e7.11.1. Transformations of Random Vectors 305\u003c\/p\u003e \u003cp\u003e7.11.2. Maximum Likelihood Estimation 308\u003c\/p\u003e \u003cp\u003e7.11.3. Comparison of Two Unbiased Estimators 310\u003c\/p\u003e \u003cp\u003e7.11.4. Best Linear Unbiased Estimation 311\u003c\/p\u003e \u003cp\u003e7.11.5. Optimal Choice of Sample Sizes in Stratified Sampling 313\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 315\u003c\/p\u003e \u003cp\u003eExercises 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Optimization in Statistics 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. The Gradient Methods 329\u003c\/p\u003e \u003cp\u003e8.1.1. The Method of Steepest Descent 329\u003c\/p\u003e \u003cp\u003e8.1.2. The Newton_Raphson Method 331\u003c\/p\u003e \u003cp\u003e8.1.3. The Davidon_Fletcher_Powell Method 331\u003c\/p\u003e \u003cp\u003e8.2. The Direct Search Methods 332\u003c\/p\u003e \u003cp\u003e8.2.1. The Nelder_Mead Simplex Method 332\u003c\/p\u003e \u003cp\u003e8.2.2. Price’s Controlled Random Search Procedure 336\u003c\/p\u003e \u003cp\u003e8.2.3. The Generalized Simulated Annealing Method 338\u003c\/p\u003e \u003cp\u003e8.3. Optimization Techniques in Response Surface Methodology 339\u003c\/p\u003e \u003cp\u003e8.3.1. The Method of Steepest Ascent 340\u003c\/p\u003e \u003cp\u003e8.3.2. The Method of Ridge Analysis 343\u003c\/p\u003e \u003cp\u003e8.3.3. Modified Ridge Analysis 350\u003c\/p\u003e \u003cp\u003e8.4. Response Surface Designs 355\u003c\/p\u003e \u003cp\u003e8.4.1. First-Order Designs 356\u003c\/p\u003e \u003cp\u003e8.4.2. Second-Order Designs 358\u003c\/p\u003e \u003cp\u003e8.4.3. Variance and Bias Design Criteria 359\u003c\/p\u003e \u003cp\u003e8.5. Alphabetic Optimality of Designs 362\u003c\/p\u003e \u003cp\u003e8.6. Designs for Nonlinear Models 367\u003c\/p\u003e \u003cp\u003e8.7. Multiresponse Optimization 370\u003c\/p\u003e \u003cp\u003e8.8. Maximum Likelihood Estimation and the EM Algorithm 372\u003c\/p\u003e \u003cp\u003e8.8.1. The EM Algorithm 375\u003c\/p\u003e \u003cp\u003e8.9. Minimum Norm Quadratic Unbiased Estimation of Variance Components 378\u003c\/p\u003e \u003cp\u003e8.10. Scheff´e’s Confidence Intervals 382\u003c\/p\u003e \u003cp\u003e8.10.1. The Relation of Scheff´e’s Confidence Intervals to the F-Test 385\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 391\u003c\/p\u003e \u003cp\u003eExercises 395\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Approximation of Functions 403\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1. Weierstrass Approximation 403\u003c\/p\u003e \u003cp\u003e9.2. Approximation by Polynomial Interpolation 410\u003c\/p\u003e \u003cp\u003e9.2.1. The Accuracy of Lagrange Interpolation 413\u003c\/p\u003e \u003cp\u003e9.2.2. A Combination of Interpolation and Approximation 417\u003c\/p\u003e \u003cp\u003e9.3. Approximation by Spline Functions 418\u003c\/p\u003e \u003cp\u003e9.3.1. Properties of Spline Functions 418\u003c\/p\u003e \u003cp\u003e9.3.2. Error Bounds for Spline Approximation 421\u003c\/p\u003e \u003cp\u003e9.4. Applications in Statistics 422\u003c\/p\u003e \u003cp\u003e9.4.1. Approximate Linearization of Nonlinear Models by Lagrange Interpolation 422\u003c\/p\u003e \u003cp\u003e9.4.2. Splines in Statistics 428\u003c\/p\u003e \u003cp\u003e9.4.2.1. The Use of Cubic Splines in Regression 428\u003c\/p\u003e \u003cp\u003e9.4.2.2. Designs for Fitting Spline Models 430\u003c\/p\u003e \u003cp\u003e9.4.2.3. Other Applications of Splines in Statistics 431\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 432\u003c\/p\u003e \u003cp\u003eExercises 434\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Orthogonal Polynomials 437\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1. Introduction 437\u003c\/p\u003e \u003cp\u003e10.2. Legendre Polynomials 440\u003c\/p\u003e \u003cp\u003e10.2.1. Expansion of a Function Using Legendre Polynomials 442\u003c\/p\u003e \u003cp\u003e10.3. Jacobi Polynomials 443\u003c\/p\u003e \u003cp\u003e10.4. Chebyshev Polynomials 444\u003c\/p\u003e \u003cp\u003e10.4.1. Chebyshev Polynomials of the First Kind 444\u003c\/p\u003e \u003cp\u003e10.4.2. Chebyshev Polynomials of the Second Kind 445\u003c\/p\u003e \u003cp\u003e10.5. Hermite Polynomials 447\u003c\/p\u003e \u003cp\u003e10.6. Laguerre Polynomials 451\u003c\/p\u003e \u003cp\u003e10.7. Least-Squares Approximation with Orthogonal Polynomials 453\u003c\/p\u003e \u003cp\u003e10.8. Orthogonal Polynomials Defined on a Finite Set 455\u003c\/p\u003e \u003cp\u003e10.9. Applications in Statistics 456\u003c\/p\u003e \u003cp\u003e10.9.1. Applications of Hermite Polynomials 456\u003c\/p\u003e \u003cp\u003e10.9.1.1. Approximation of Density Functions and Quantiles of Distributions 456\u003c\/p\u003e \u003cp\u003e10.9.1.2. Approximation of a Normal Integral 460\u003c\/p\u003e \u003cp\u003e10.9.1.3. Estimation of Unknown Densities 461\u003c\/p\u003e \u003cp\u003e10.9.2. Applications of Jacobi and Laguerre Polynomials 462\u003c\/p\u003e \u003cp\u003e10.9.3. Calculation of Hypergeometric Probabilities Using Discrete Chebyshev Polynomials 462\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 464\u003c\/p\u003e \u003cp\u003eExercises 466\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Fourier Series 471\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1. Introduction 471\u003c\/p\u003e \u003cp\u003e11.2. Convergence of Fourier Series 475\u003c\/p\u003e \u003cp\u003e11.3. Differentiation and Integration of Fourier Series 483\u003c\/p\u003e \u003cp\u003e11.4. The Fourier Integral 488\u003c\/p\u003e \u003cp\u003e11.5. Approximation of Functions by Trigonometric Polynomials 495\u003c\/p\u003e \u003cp\u003e11.5.1. Parseval’s Theorem 496\u003c\/p\u003e \u003cp\u003e11.6. The Fourier Transform 497\u003c\/p\u003e \u003cp\u003e11.6.1. Fourier Transform of a Convolution 499\u003c\/p\u003e \u003cp\u003e11.7. Applications in Statistics 500\u003c\/p\u003e \u003cp\u003e11.7.1. Applications in Time Series 500\u003c\/p\u003e \u003cp\u003e11.7.2. Representation of Probability Distributions 501\u003c\/p\u003e \u003cp\u003e11.7.3. Regression Modeling 504\u003c\/p\u003e \u003cp\u003e11.7.4. The Characteristic Function 505\u003c\/p\u003e \u003cp\u003e11.7.4.1. Some Properties of Characteristic Functions 510\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 510\u003c\/p\u003e \u003cp\u003eExercises 512\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12. Approximation of Integrals 517\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1. The Trapezoidal Method 517\u003c\/p\u003e \u003cp\u003e12.1.1. Accuracy of the Approximation 518\u003c\/p\u003e \u003cp\u003e12.2. Simpson’s Method 521\u003c\/p\u003e \u003cp\u003e12.3. Newton_Cotes Methods 523\u003c\/p\u003e \u003cp\u003e12.4. Gaussian Quadrature 524\u003c\/p\u003e \u003cp\u003e12.5. Approximation over an Infinite Interval 528\u003c\/p\u003e \u003cp\u003e12.6. The Method of Laplace 531\u003c\/p\u003e \u003cp\u003e12.7. Multiple Integrals 533\u003c\/p\u003e \u003cp\u003e12.8. The Monte Carlo Method 535\u003c\/p\u003e \u003cp\u003e12.8.1. Variation Reduction 537\u003c\/p\u003e \u003cp\u003e12.8.2. Integrals in Higher Dimensions 540\u003c\/p\u003e \u003cp\u003e12.9. Applications in Statistics 541\u003c\/p\u003e \u003cp\u003e12.9.1. The Gauss_Hermite Quadrature 542\u003c\/p\u003e \u003cp\u003e12.9.2. Minimum Mean Squared Error Quadrature 543\u003c\/p\u003e \u003cp\u003e12.9.3. Moments of a Ratio of Quadratic Forms 546\u003c\/p\u003e \u003cp\u003e12.9.4. Laplace’s Approximation in Bayesian Statistics 548\u003c\/p\u003e \u003cp\u003e12.9.5. Other Methods of Approximating Integrals in Statistics 549\u003c\/p\u003e \u003cp\u003eFurther Reading and Annotated Bibliography 550\u003c\/p\u003e \u003cp\u003eExercises 552\u003c\/p\u003e \u003cp\u003eAppendix. Solutions to Selected Exercises 557\u003c\/p\u003e \u003cp\u003eGeneral Bibliography 652\u003c\/p\u003e \u003cp\u003eIndex 665\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402582860119,"sku":"9780471391043","price":143.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471391043.jpg?v=1730480845"},{"product_id":"mathematical-analysis-of-deterministic-and-stochastic-problems-in-complex-media-electromagnetics-9780691142173","title":"Mathematical Analysis of Deterministic and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eElectromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. This book introduces the electromagnetics of complex media through a systematic account of their mathematical theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems.\"--Vilmos Komornik, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi       PART 1. MODELLING AND MATHEMATICAL PRELIMINARIES 1       Chapter 1. Complex Media 3   Chapter 2. The Maxwell Equations and Constitutive Relations 9   2.1 Introduction 9   2.2 Fundamentals 9   2.3 Constitutive relations 13   2.4 The Maxwell equations in complex media: A variety of problems 23       Chapter 3. Spaces and Operators 38   3.1 Introduction 38   3.2 Function spaces 38   3.3 Standard difierential and trace operators 45   3.4 Function spaces for electromagnetics 48   3.5 Traces 51   3.6 Various decompositions 52   3.7 Compact embeddings 53   3.8 The operators of vector analysis revisited 54   3.9 The Maxwell operator 56       PART 2. TIME-HARMONIC DETERMINISTIC PROBLEMS 59       Chapter 4. Well Posedness 61   4.1 Introduction 61   4.2 Solvability of the interior problem 62   4.3 The eigenvalue problem 68   4.4 Low chirality behaviour 70   4.5 Comments on exterior domain problems 74   4.6 Towards numerics 77       Chapter 5. Scattering Problems: Beltrami Fields and Solvability 83   5.1 Introduction 83   5.2 Elliptic, circular and linear polarisation of waves 84   5.3 Beltrami fields - The Bohren decomposition 86   5.4 Scattering problems: Formulation 88   5.5 An introduction to BIEs 91   5.6 Properties of Beltrami fields 96   5.7 Solvability 99   5.8 Generalised Muller's BIEs 106   5.9 Low chirality approximations 108   5.10 Miscellanea 109       Chapter 6. Scattering Problems: A Variety of Topics 112   6.1 Introduction 112   6.2 Important concepts of scattering theory 113   6.3 Back to chiral media: Scattering relations and the far-field operator 118   6.4 Using dyadics 124   6.5 Herglotz wave functions 129   6.6 Domain derivative 136   6.7 Miscellanea 140       PART 3. TIME-DEPENDENT DETERMINISTIC PROBLEMS 149       Chapter 7. Well Posedness 151   7.1 Introduction 151   7.2 The Maxwell equations in the time domain 151   7.3 Functional framework and assumptions 152   7.4 Solvability 153   7.5 Other possible approaches to solvability 158   7.6 Miscellanea 162       Chapter 8. Controllability 163   8.1 Introduction 163   8.2 Formulation 163   8.3 Controllability of achiral media: The Hilbert Uniqueness method 165   8.4 The forward and backward problems 167   8.5 Controllability: Complex media 174   8.6 Miscellanea 176       Chapter 9. Homogenisation 180   9.1 Introduction 180   9.2 Formulation 181   9.3 A formal two-scale expansion 184   9.4 The optical response region 188   9.5 General bianisotropic media 199   9.6 Miscellanea 207       Chapter 10. Towards a Scattering Theory 212   10.1 Introduction 212   10.2 Formulation 213   10.3 Some basic strategies 214   10.4 On the construction of solutions 217   10.5 Wave operators and their construction 220   10.6 Complex media electromagnetics 225   10.7 Miscellanea 229       Chapter 11. Nonlinear Problems 231   11.1 Introduction 231   11.2 Formulation 231   11.3 Well posedness of the model 232   11.4 Miscellanea 241       PART 4. STOCHASTIC PROBLEMS 245       Chapter 12. Well Posedness 247   12.1 Introduction 247   12.2 Maxwell equations for random media 248   12.3 Functional setting 249   12.4 Well posedness 250   12.5 Other possible approaches to solvability 255   12.6 Miscellanea 261      Chapter 13. Controllability 263   13.1 Introduction 263   13.2 Formulation 263   13.3 Subtleties of stochastic controllability 264   13.4 Approximate controllability I: Random PDEs 266   13.5 Approximate controllability II: BSPDEs 269   13.6 Miscellanea 272       Chapter 14. Homogenisation 275   14.1 Introduction 275   14.2 Ergodic media 276   14.3 Formulation 279   14.4 A formal two-scale expansion 282   14.5 Homogenisation of the Maxwell system 284   14.6 Miscellanea 288       PART 5. APPENDICES 291       Appendix A. Some Facts from Functional Analysis 293   A.1 Duality 293   A.2 Strong, weak and weak-* convergence 295   A.3 Calculus in Banach spaces 297   A.4 Basic elements of spectral theory 300   A.5 Compactness criteria 303   A.6 Compact operators 304   A.7 The Banach-Steinhaus theorem 308   A.8 Semigroups and the Cauchy problem 308   A.9 Some fixed point theorems 312   A.10 The Lax-Milgram lemma 313   A.11 Gronwall's inequality 314   A.12 Nonlinear operators 315       Appendix B. Some Facts from Stochastic Analysis 316   B.1 Probability in Hilbert spaces 316   B.2 Stochastic processes and random fields 318   B.3 Gaussian measures 319   B.4 The Q- and the cylindrical Wiener process 320   B.5 The Ito integral 321   B.6 Ito formula 324   B.7 Stochastic convolution 325   B.8 SDEs in Hilbert spaces 325   B.9 Martingale representation theorem 326       Appendix C. Some Facts from Elliptic Homogenisation Theory 327   C.1 Spaces of periodic functions 327   C.2 Compensated compactness 329   C.3 Homogenisation of elliptic equations 329   C.4 Random elliptic homogenisation theory 332   Appendix D. Some Facts from Dyadic Analysis (by George Dassios) 334   Appendix E. Notation and abbreviations 341       Bibliography 343   Index 377","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403768930647,"sku":"9780691142173","price":100.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691142173.jpg?v=1730484487"},{"product_id":"partial-differential-equations-an-introduction-to-theory-and-applications-9780691161297","title":"Partial Differential Equations  An Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book ser\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book is unique in that it provides a very comprehensive introduction to the theory of PDEs embedded in specific relevant applications in the field.\"--Choice \"The authors provide not only a clear and rigorous explanation of the more elementary theoretical aspects of partial differential equations, but they are also concerned with tools of applied mathematics in the setting of partial differential equations... This reviewer warmly recommends this volume to mathematical university libraries.\"--Vicentiu D. Radulescu, Zentralblatt MATH","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403805172055,"sku":"9780691161297","price":68.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691161297.jpg?v=1730484599"},{"product_id":"zombies-and-calculus-9780691161907","title":"Zombies and Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eHow can calculus help you survive the zombie apocalypse? Colin Adams, humor columnist for the Mathematical Intelligencer and one of today's most outlandish and entertaining popular math writers, demonstrates how in this zombie adventure novel. Zombies and Calculus is the account of Craig Williams, a math professor at a small liberal arts college i\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Romance! Danger! Calculus! Zombies! Adams (How to Ace Calculus), professor of mathematics at Williams College and humor columnist for The Mathematical Intelligencer, takes readers on an apocalyptic and educational adventure that's also a Spielbergian sci-fi thriller... Adams keeps the in-story math both appropriate and accessible, saving in-depth discussion for appendices at the end. Calculus fans looking for 'real-world' applications woven into a nail-biter of a story, chock-full of narrow escapes, betrayals, some plucky kids, the family dog, and even a romantic subplot, will delight in this fun, and funny pop-math book.\"--Publishers Weekly starred review \"The author didn't intend to write a classic horror novel, he intended to write one that explained the ideas of calculus and differential equations (particularly the latter) in a humorous and unusual setting. He has succeeded admirably. This is a book that can be enjoyed by both students and by faculty members seeking a way to spice up their lectures.\"--Mark Hunacek, MAA Reviews \"You'll laugh! You'll cry! You'll use calculus! So much for kids who say, 'When am I ever going to use calculus?' When you're trying to survive the zombie apocalypse, that's when.\"--Nancy Szokan, Washington Post \"A fun idea, quite well realized.\"--M.A.Orthofer, Complete Review \"The book well deserves attention from not squeamish math instructors and a wider audience of intelligent readers, curious of a new literary genre that mixes storytelling with gentle mathematical instruction.\"--Alexander Bogomolny, CTK Insights \"Whether you agree or disagree with the idea of mixing zombies with calculus, Adams is a craftsman of the first order. Zombies and Calculus has everything: calculus, calculation of force, statistics, normal deviation, word play, heroics, romance, slapstick, and zombies. Two bloody thumbs up!\"--Robert Schaefer, New York Journal of Books \"The unusual and clearly explained mathematical set-pieces are appealing... I will be recommending this book to colleagues. Let's hope they're not squeamish.\"--Noel-Ann Bradshaw, Times Higher Education \"Adams combines mathematics and zombies in an exciting, humorous way... Zombies and Calculus would be a helpful supplemental text for a student currently studying calculus as it applies the concepts in a situation--however unrealistic--that makes it easier to understand.\"--Tara Creel, Deseret News \"I have never met a novel in which the hero is actually teaching calculus to the ones he just rescued in between blowing out the little bit of brains from zombie heads, and smashing cars with a snow plough. Quite a reading experience.\"--Adhemar Bultheel, European Mathematical Society \"Adams is clever to employ a zombie apocalypse scenario to demonstrate the usefulness of calculus and mathematics more broadly.\"--Carrie Bengston, Science Book A Day \"Highly recommended for those just being introduced to calculus, or those who need a user-friendly recap of the basics. It may just help them survive--their education, that is, rather than a zombie attack!\"--Rob Ashmore, Mathematics Today \"Adams tells his tale with gore and humor. If you are a fan of zombies and enjoy offbeat applications of mathematics, this book is for you.\"--Joseph Bettina, Mathematics Teacher \"I think that the book is very successful at doing what it was intended to do, namely to demonstrate the usefulness and relevance of what may seem at the first glance to be very abstract maths while teaching it in an engaging way. I would struggle to name another book that manages to couch the process of solving ODEs in quite so entertaining and humorous a manner.\"--Andrew Simmons, Mathematical Gazette\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction 1  CHAPTER 1 Hour 6 3  CHAPTER 2 Hour 7 19  CHAPTER 3 Hour 7 1\/2 32  CHAPTER 4 Hour 7 3\/4 48  CHAPTER 5 Hour 8 63  CHAPTER 6 Hour 9 80  CHAPTER 7 Hour 10 95  CHAPTER 8 Hour 18 111  CHAPTER 9 Hour 24 137  Epilogue 152  APPENDIX A Continuing the Conversations 155  APPENDIX B A Brief Review of Calculus as Explained to Connor by Ellie 191  Acknowledgments 223  Bibliography 225  Index 227","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403806253399,"sku":"9780691161907","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691161907.jpg?v=1730484602"},{"product_id":"the-calculus-of-happiness-9780691168630","title":"The Calculus of Happiness","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"There are plenty of books about managing your wealth, but The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love, by Oscar Fernandez of Princeton University Press, sounds intriguing.\"--Matthew Partridge, Money Week \"[E]ngaging... Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant.\"--Jason M. Graham, MAA Reviews \"Brilliant... Where Fernandez's book scores highly is that it goes beyond being a typical self-help manual for the numerate, by presenting example after example of how mathematical topics such as probability, game theory and exponential functions really do make sense of a world that can sometimes seem so subjective. It's also an easy-going analysis of those areas in life that get brushed under the carpet, to be attended to another day. Once you realise it all boils down to maths, you will wake up happier, wealthier and healthier tomorrow morning, and we have Oscar E. Fernandez to thank for that.\"Nick Smith, Engineering \u0026amp; Technology\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix  Math Topics Covered by Chapter xiii  I: A Healthier You Is Just a Few Equations Away 1  1 How Many Calories Should You Eat Each Day? 3  1.1 The Linear Functions Hidden in Your Diet 4  1.2 The Mathematics of Metabolism 8  1.3 Burn Those Calories! Work Those Quads! 11  1.4 The Calories Required to Digest Food 14  2 Live Longer (and Be Healthier) by Eating the Right Foods 20  2.1 A Game of Macronutrient Musical Chairs 20  2.2 How to Eat More and Be Healthier: Energy Density 29  2.3 Live Long(er) and Prosper with theWaist-Height Ratio 34  II: A Mathematician's Guide to Managing Your Money 41  3 Dissecting Your Monthly Budget 43  3.1 The Return of the King (the Linear Function) 44  3.2 To Expenses, and Beyond! 49  3.3 How Many YearsWill It Take You to Reach Financial Independence? 62  4 How to Beat Wall Street at Its Own Game 69  4.1 How to Make 15% a Year, Guaranteed 70  4.2 The Safest Investments 71  4.3 Quantifying Investment Risk and Return 73  4.4 Stocks, Bonds, and the \"All-Weather\" Portfolio 77  III: Looking for Love? There May Be an Equation for That 87  5 Finding \"The 1\" 89  5.1 What the Search for Aliens Can Teach You about FindingYour Soulmate 89  5.2 Why Hiring a Secretary Is Like Dating 92  5.3 The Stable Matching Problem 97  6 Living Happily Ever After with \"The 1\" 103  6.1 Your Relationship as a Dynamical System 104  6.2 Need Help Making a Joint Decision? There's an Equation for That 108  6.3 How Psychologists Use Math to Predict Divorce 113  Epilogue 118  Acknowledgments 120  Appendix A: Background Content 121  Appendix 1 123  Appendix 2 128  Appendix 3 130  Appendix 4 141  Appendix 5 143  Appendix 6 144  Bibliography 151  Index 157","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403822473559,"sku":"9780691168630","price":22.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691168630.jpg?v=1730484647"},{"product_id":"the-calculus-gallery-9780691182858","title":"The Calculus Gallery","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This is a book that should be part of the personal library of any mathematician.\"\u003cb\u003e---Mark Hunacek, \u003ci\u003eMathematical Gazette\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403864023383,"sku":"9780691182858","price":15.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691182858.jpg?v=1730484748"},{"product_id":"visual-differential-geometry-and-forms-a-mathematical-drama-in-five-acts-9780691203690","title":"Visual Differential Geometry and Forms  A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Finalist for the PROSE Award in Mathematics, Association of American Publishers\"\u003cbr\u003e\"Needham proposes to provide a truly geometric 'visual' explication of differential geometry, and he succeeds brilliantly. I know nothing like it in the literature.\"\u003cb\u003e---Frank Morgan, \u003ci\u003eEMS Magazine\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[The] book offers a truly unique and original take on differential geometry, and it amply deserves inclusion within the pantheon of textbook deities.\"\u003cb\u003e---Eric Poisson, \u003ci\u003eNotices of the AMS\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This is a valuable and beautifully created guide to what can at first seem a confusing area of mathematical physics. There are other contenders that try to teach this subject, but this is the best that I have come across so far and I will continue to enjoy learning from it (and almost certainly teaching from it) over the coming years, I am sure.\"\u003cb\u003e---Jonathan Shock, \u003ci\u003eMathemafrica\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[Proactively] rethinks the way this important area of mathematics should be considered and taught.\" * MathSciNet *\u003cbr\u003e\"The book is a remarkable and highly original approach to the basic stem of differential geometry. And that mathematical trunk has roots and branches in so many other unexpected yet related subjects, each of which can be equally well approached from the same geometrical point of view.\"\u003cb\u003e---Adhemar Bultheel, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[\u003ci\u003eVisual Differential Geometry and Forms\u003c\/i\u003e] its peers. It is fun to read and provides a unique and intuitive approach to differential geometry. The author’s passion for the subject is evident throughout the book. Although Needham’s approach is unorthodox, it is rewarding, and complements the exposition found in standard textbooks.\"\u003cb\u003e---Sean M. Eli \u0026amp; Krešmir Josić, \u003ci\u003eSIAM Review\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403892040023,"sku":"9780691203690","price":100.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691203690.jpg?v=1730484813"},{"product_id":"calculus-for-dummies-9781119293491","title":"Calculus For Dummies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus For Dummies, 2nd Edition (9781119293491) was previously published as Calculus For Dummies, 2nd Edition (9781118791295). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 1: An Overview of Calculus\u003c\/b\u003e\u003cb\u003e 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1: What Is Calculus? 7\u003c\/p\u003e \u003cp\u003eChapter 2: The Two Big Ideas of Calculus: Differentiation and Integration — plus Infinite Series 13\u003c\/p\u003e \u003cp\u003eChapter 3: Why Calculus Works 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 2: Warming Up with Calculus Prerequisites \u003c\/b\u003e\u003cb\u003e27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 4: Pre-Algebra and Algebra Review 29\u003c\/p\u003e \u003cp\u003eChapter 5: Funky Functions and Their Groovy Graphs 43\u003c\/p\u003e \u003cp\u003eChapter 6: The Trig Tango 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 3: Limits \u003c\/b\u003e\u003cb\u003e73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 7: Limits and Continuity 75\u003c\/p\u003e \u003cp\u003eChapter 8: Evaluating Limits 89\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 4: Differentiation\u003c\/b\u003e\u003cb\u003e 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 9: Differentiation Orientation 107\u003c\/p\u003e \u003cp\u003eChapter 10: Differentiation Rules — Yeah, Man, It Rules 127\u003c\/p\u003e \u003cp\u003eChapter 11: Differentiation and the Shape of Curves 147\u003c\/p\u003e \u003cp\u003eChapter 12: Your Problems Are Solved: Differentiation to the Rescue! 171\u003c\/p\u003e \u003cp\u003eChapter 13: More Differentiation Problems: Going Off on a Tangent 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 5: Integration and Infinite Series\u003c\/b\u003e\u003cb\u003e 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 14: Intro to Integration and Approximating Area 209\u003c\/p\u003e \u003cp\u003eChapter 15: Integration: It’s Backwards Differentiation 233\u003c\/p\u003e \u003cp\u003eChapter 16: Integration Techniques for Experts 263\u003c\/p\u003e \u003cp\u003eChapter 17: Forget Dr Phil: Use the Integral to Solve Problems 285\u003c\/p\u003e \u003cp\u003eChapter 18: Taming the Infinite with Improper Integrals 303\u003c\/p\u003e \u003cp\u003eChapter 19: Infinite Series 315\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 6: The Part of Tens\u003c\/b\u003e\u003cb\u003e 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 20: Ten Things to Remember 341\u003c\/p\u003e \u003cp\u003eChapter 21: Ten Things to Forget 345\u003c\/p\u003e \u003cp\u003eChapter 22: Ten Things You Can’t Get Away With 349\u003c\/p\u003e \u003cp\u003eIndex 353\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407030100311,"sku":"9781119293491","price":15.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119293491.jpg?v=1730497932"},{"product_id":"mathematical-analysis-and-applications-9781119414346","title":"Mathematical Analysis and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAn authoritative text that presents the current problems, theories, and applications of mathematical analysis research\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematical Analysis and Applications: Selected Topics\u003c\/i\u003e offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and FussCatalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authorsa noted team of international researchers in the field highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to f\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAbout the Editors xxi\u003c\/p\u003e \u003cp\u003eList of Contributors xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Spaces of Asymptotically Developable Functions and Applications 1\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSergio Alejandro Carrillo Torres and Jorge Mozo Fernández\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction and Some Notations 1\u003c\/p\u003e \u003cp\u003e1.2 Strong Asymptotic Expansions 2\u003c\/p\u003e \u003cp\u003e1.3 Monomial Asymptotic Expansions 7\u003c\/p\u003e \u003cp\u003e1.4 Monomial Summability for Singularly Perturbed Differential Equations 13\u003c\/p\u003e \u003cp\u003e1.5 Pfaffian Systems 15\u003c\/p\u003e \u003cp\u003eReferences 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Duality for Gaussian Processes from Random Signed Measures 23\u003cbr\u003e\u003c\/b\u003e\u003ci\u003ePalle E.T. Jorgensen and Feng Tian\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 23\u003c\/p\u003e \u003cp\u003e2.2 Reproducing Kernel Hilbert Spaces (RKHSs) in the Measurable Category 24\u003c\/p\u003e \u003cp\u003e2.3 Applications to Gaussian Processes 30\u003c\/p\u003e \u003cp\u003e2.4 Choice of Probability Space 34\u003c\/p\u003e \u003cp\u003e2.5 A Duality 37\u003c\/p\u003e \u003cp\u003e2.A Stochastic Processes 40\u003c\/p\u003e \u003cp\u003e2.B Overview of Applications of RKHSs 45\u003c\/p\u003e \u003cp\u003eAcknowledgments 50\u003c\/p\u003e \u003cp\u003eReferences 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Many-Body Wave Scattering Problems for Small Scatterers and Creating Materials with a Desired Refraction Coefficient 57\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAlexander G. Ramm\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 57\u003c\/p\u003e \u003cp\u003e3.2 Derivation of the Formulas for One-Body Wave Scattering Problems 62\u003c\/p\u003e \u003cp\u003e3.3 Many-Body Scattering Problem 65\u003c\/p\u003e \u003cp\u003e3.3.1 The Case of Acoustically Soft Particles 68\u003c\/p\u003e \u003cp\u003e3.3.2 Wave Scattering by Many Impedance Particles 70\u003c\/p\u003e \u003cp\u003e3.4 Creating Materials with a Desired Refraction Coefficient 71\u003c\/p\u003e \u003cp\u003e3.5 Scattering by Small Particles Embedded in an Inhomogeneous Medium 72\u003c\/p\u003e \u003cp\u003e3.6 Conclusions 72\u003c\/p\u003e \u003cp\u003eReferences 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Generalized Convex Functions and their Applications 77\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAdem Kiliçman and Wedad Saleh\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Brief Introduction 77\u003c\/p\u003e \u003cp\u003e4.2 Generalized E-Convex Functions 78\u003c\/p\u003e \u003cp\u003e4.3 \u003ci\u003eE\u003c\/i\u003e\u003csup\u003e𝛼\u003c\/sup\u003e-Epigraph 84\u003c\/p\u003e \u003cp\u003e4.4 Generalized s-Convex Functions 85\u003c\/p\u003e \u003cp\u003e4.5 Applications to Special Means 96\u003c\/p\u003e \u003cp\u003eReferences 98\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Some Properties and Generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers 101\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eFeng Qi and Bai-Ni Guo\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Catalan Numbers 101\u003c\/p\u003e \u003cp\u003e5.1.1 A Definition of the Catalan Numbers 101\u003c\/p\u003e \u003cp\u003e5.1.2 The History of the Catalan Numbers 101\u003c\/p\u003e \u003cp\u003e5.1.3 A Generating Function of the Catalan Numbers 102\u003c\/p\u003e \u003cp\u003e5.1.4 Some Expressions of the Catalan Numbers 102\u003c\/p\u003e \u003cp\u003e5.1.5 Integral Representations of the Catalan Numbers 103\u003c\/p\u003e \u003cp\u003e5.1.6 Asymptotic Expansions of the Catalan Function 104\u003c\/p\u003e \u003cp\u003e5.1.7 Complete Monotonicity of the Catalan Numbers 105\u003c\/p\u003e \u003cp\u003e5.1.8 Inequalities of the Catalan Numbers and Function 106\u003c\/p\u003e \u003cp\u003e5.1.9 The Bell Polynomials of the Second Kind and the Bessel Polynomials 109\u003c\/p\u003e \u003cp\u003e5.2 The Catalan–Qi Function 111\u003c\/p\u003e \u003cp\u003e5.2.1 The Fuss Numbers 111\u003c\/p\u003e \u003cp\u003e5.2.2 A Definition of the Catalan–Qi Function 111\u003c\/p\u003e \u003cp\u003e5.2.3 Some Identities of the Catalan–Qi Function 112\u003c\/p\u003e \u003cp\u003e5.2.4 Integral Representations of the Catalan–Qi Function 114\u003c\/p\u003e \u003cp\u003e5.2.5 Asymptotic Expansions of the Catalan–Qi Function 115\u003c\/p\u003e \u003cp\u003e5.2.6 Complete Monotonicity of the Catalan–Qi Function 116\u003c\/p\u003e \u003cp\u003e5.2.7 Schur-Convexity of the Catalan–Qi Function 118\u003c\/p\u003e \u003cp\u003e5.2.8 Generating Functions of the Catalan–Qi Numbers 118\u003c\/p\u003e \u003cp\u003e5.2.9 A Double Inequality of the Catalan–Qi Function 118\u003c\/p\u003e \u003cp\u003e5.2.10 The \u003ci\u003eq\u003c\/i\u003e-Catalan–Qi Numbers and Properties 119\u003c\/p\u003e \u003cp\u003e5.2.11 The Catalan Numbers and the \u003ci\u003ek\u003c\/i\u003e-Gamma and \u003ci\u003ek\u003c\/i\u003e-Beta Functions 119\u003c\/p\u003e \u003cp\u003e5.2.12 Series Identities Involving the Catalan Numbers 119\u003c\/p\u003e \u003cp\u003e5.3 The Fuss–Catalan Numbers 119\u003c\/p\u003e \u003cp\u003e5.3.1 A Definition of the Fuss–Catalan Numbers 119\u003c\/p\u003e \u003cp\u003e5.3.2 A Product-Ratio Expression of the Fuss–Catalan Numbers 120\u003c\/p\u003e \u003cp\u003e5.3.3 Complete Monotonicity of the Fuss–Catalan Numbers 120\u003c\/p\u003e \u003cp\u003e5.3.4 A Double Inequality for the Fuss–Catalan Numbers 121\u003c\/p\u003e \u003cp\u003e5.4 The Fuss–Catalan–Qi Function 121\u003c\/p\u003e \u003cp\u003e5.4.1 A Definition of the Fuss–Catalan–Qi Function 121\u003c\/p\u003e \u003cp\u003e5.4.2 A Product-Ratio Expression of the Fuss–Catalan–Qi Function 122\u003c\/p\u003e \u003cp\u003e5.4.3 Integral Representations of the Fuss–Catalan–Qi Function 123\u003c\/p\u003e \u003cp\u003e5.4.4 Complete Monotonicity of the Fuss–Catalan–Qi Function 124\u003c\/p\u003e \u003cp\u003e5.5 Some Properties for Ratios of Two Gamma Functions 124\u003c\/p\u003e \u003cp\u003e5.5.1 An Integral Representation and Complete Monotonicity 125\u003c\/p\u003e \u003cp\u003e5.5.2 An Exponential Expansion for the Ratio of Two Gamma Functions 125\u003c\/p\u003e \u003cp\u003e5.5.3 A Double Inequality for the Ratio of Two Gamma Functions 125\u003c\/p\u003e \u003cp\u003e5.6 Some New Results on the Catalan Numbers 126\u003c\/p\u003e \u003cp\u003e5.7 Open Problems 126\u003c\/p\u003e \u003cp\u003eAcknowledgments 127\u003c\/p\u003e \u003cp\u003eReferences 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Trace Inequalities of Jensen Type for Self-adjoint Operators in Hilbert Spaces: A Survey of Recent Results 135\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSilvestru Sever Dragomir\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 135\u003c\/p\u003e \u003cp\u003e6.1.1 Jensen’s Inequality 135\u003c\/p\u003e \u003cp\u003e6.1.2 Traces for Operators in Hilbert Spaces 138\u003c\/p\u003e \u003cp\u003e6.2 Jensen’s Type Trace Inequalities 141\u003c\/p\u003e \u003cp\u003e6.2.1 Some Trace Inequalities for Convex Functions 141\u003c\/p\u003e \u003cp\u003e6.2.2 Some Functional Properties 145\u003c\/p\u003e \u003cp\u003e6.2.3 Some Examples 151\u003c\/p\u003e \u003cp\u003e6.2.4 More Inequalities for Convex Functions 154\u003c\/p\u003e \u003cp\u003e6.3 Reverses of Jensen’s Trace Inequality 157\u003c\/p\u003e \u003cp\u003e6.3.1 A Reverse of Jensen’s Inequality 157\u003c\/p\u003e \u003cp\u003e6.3.2 Some Examples 163\u003c\/p\u003e \u003cp\u003e6.3.3 Further Reverse Inequalities for Convex Functions 165\u003c\/p\u003e \u003cp\u003e6.3.4 Some Examples 169\u003c\/p\u003e \u003cp\u003e6.3.5 Reverses of Hölder’s Inequality 174\u003c\/p\u003e \u003cp\u003e6.4 Slater’s Type Trace Inequalities 177\u003c\/p\u003e \u003cp\u003e6.4.1 Slater’s Type Inequalities 177\u003c\/p\u003e \u003cp\u003e6.4.2 Further Reverses 180\u003c\/p\u003e \u003cp\u003eReferences 188\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Spectral Synthesis and Its Applications 193\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eLászló Székelyhidi\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 193\u003c\/p\u003e \u003cp\u003e7.2 Basic Concepts and Function Classes 195\u003c\/p\u003e \u003cp\u003e7.3 Discrete Spectral Synthesis 203\u003c\/p\u003e \u003cp\u003e7.4 Nondiscrete Spectral Synthesis 217\u003c\/p\u003e \u003cp\u003e7.5 Spherical Spectral Synthesis 219\u003c\/p\u003e \u003cp\u003e7.6 Spectral Synthesis on Hypergroups 238\u003c\/p\u003e \u003cp\u003e7.7 Applications 248\u003c\/p\u003e \u003cp\u003eAcknowledgments 252\u003c\/p\u003e \u003cp\u003eReferences 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Various Ulam–Hyers Stabilities of Euler–Lagrange–Jensen General (a, b; k = a + b)-Sextic Functional Equations 255\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJohn Michael Rassias and Narasimman Pasupathi\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Brief Introduction 255\u003c\/p\u003e \u003cp\u003e8.2 General Solution of Euler–Lagrange–Jensen General\u003c\/p\u003e \u003cp\u003e(\u003ci\u003ea, b; k = a + b\u003c\/i\u003e)-Sextic Functional Equation 257\u003c\/p\u003e \u003cp\u003e8.3 Stability Results in Banach Space 258\u003c\/p\u003e \u003cp\u003e8.3.1 Banach Space: Direct Method 258\u003c\/p\u003e \u003cp\u003e8.3.2 Banach Space: Fixed Point Method 261\u003c\/p\u003e \u003cp\u003e8.4 Stability Results in Felbin’s Type Spaces 267\u003c\/p\u003e \u003cp\u003e8.4.1 Felbin’s Type Spaces: Direct Method 268\u003c\/p\u003e \u003cp\u003e8.4.2 Felbin’s Type Spaces: Fixed Point Method 269\u003c\/p\u003e \u003cp\u003e8.5 Intuitionistic Fuzzy Normed Space: Stability Results 270\u003c\/p\u003e \u003cp\u003e8.5.1 IFNS: Direct Method 272\u003c\/p\u003e \u003cp\u003e8.5.2 IFNS: Fixed Point Method 279\u003c\/p\u003e \u003cp\u003eReferences 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 A Note on the Split Common Fixed Point Problem and its Variant Forms 283\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAdem Kiliçman and L.B. Mohammed\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 283\u003c\/p\u003e \u003cp\u003e9.2 Basic Concepts and Definitions 284\u003c\/p\u003e \u003cp\u003e9.2.1 Introduction 284\u003c\/p\u003e \u003cp\u003e9.2.2 Vector Space 284\u003c\/p\u003e \u003cp\u003e9.2.3 Hilbert Space and its Properties 286\u003c\/p\u003e \u003cp\u003e9.2.4 Bounded Linear Map and its Properties 288\u003c\/p\u003e \u003cp\u003e9.2.5 Some Nonlinear Operators 289\u003c\/p\u003e \u003cp\u003e9.2.6 Problem Formulation 294\u003c\/p\u003e \u003cp\u003e9.2.7 Preliminary Results 294\u003c\/p\u003e \u003cp\u003e9.2.8 Strong Convergence for the Split Common Fixed-Point Problems for Total Quasi-Asymptotically Nonexpansive Mappings 296\u003c\/p\u003e \u003cp\u003e9.2.9 Strong Convergence for the Split Common Fixed-Point Problems for Demicontractive Mappings 302\u003c\/p\u003e \u003cp\u003e9.2.10 Application to Variational Inequality Problems 306\u003c\/p\u003e \u003cp\u003e9.2.11 On Synchronal Algorithms for Fixed and Variational Inequality Problems in Hilbert Spaces 307\u003c\/p\u003e \u003cp\u003e9.2.12 Preliminaries 307\u003c\/p\u003e \u003cp\u003e9.3 A Note on the Split Equality Fixed-Point Problems in Hilbert Spaces 315\u003c\/p\u003e \u003cp\u003e9.3.1 Problem Formulation 315\u003c\/p\u003e \u003cp\u003e9.3.2 Preliminaries 316\u003c\/p\u003e \u003cp\u003e9.3.3 The Split Feasibility and Fixed-Point Equality Problems for Quasi-Nonexpansive Mappings in Hilbert Spaces 316\u003c\/p\u003e \u003cp\u003e9.3.4 The Split Common Fixed-Point Equality Problems for Quasi-Nonexpansive Mappings in Hilbert Spaces 320\u003c\/p\u003e \u003cp\u003e9.4 Numerical Example 322\u003c\/p\u003e \u003cp\u003e9.5 The Split Feasibility and Fixed Point Problems for Quasi-Nonexpansive Mappings in Hilbert Spaces 328\u003c\/p\u003e \u003cp\u003e9.5.1 Problem Formulation 328\u003c\/p\u003e \u003cp\u003e9.5.2 Preliminary Results 328\u003c\/p\u003e \u003cp\u003e9.6 Ishikawa-Type Extra-Gradient Iterative Methods for Quasi-Nonexpansive Mappings in Hilbert Spaces 329\u003c\/p\u003e \u003cp\u003e9.6.1 Application to Split Feasibility Problems 334\u003c\/p\u003e \u003cp\u003e9.7 Conclusion 336\u003c\/p\u003e \u003cp\u003eReferences 337\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Stabilities and Instabilities of Rational Functional Equations and Euler–Lagrange–Jensen (\u003ci\u003ea, b\u003c\/i\u003e)-Sextic Functional Equations 341\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJohn Michael Rassias, Krishnan Ravi, and Beri V. Senthil Kumar\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 341\u003c\/p\u003e \u003cp\u003e10.1.1 Growth of Functional Equations 342\u003c\/p\u003e \u003cp\u003e10.1.2 Importance of Functional Equations 342\u003c\/p\u003e \u003cp\u003e10.1.3 Functional Equations Relevant to Other Fields 343\u003c\/p\u003e \u003cp\u003e10.1.4 Definition of Functional Equation with Examples 343\u003c\/p\u003e \u003cp\u003e10.2 Ulam Stability Problem for Functional Equation 344\u003c\/p\u003e \u003cp\u003e10.2.1 𝜖-Stability of Functional Equation 344\u003c\/p\u003e \u003cp\u003e10.2.2 Stability Involving Sum of Powers of Norms 345\u003c\/p\u003e \u003cp\u003e10.2.3 Stability Involving Product of Powers of Norms 346\u003c\/p\u003e \u003cp\u003e10.2.4 Stability Involving a General Control Function 347\u003c\/p\u003e \u003cp\u003e10.2.5 Stability Involving Mixed Product–Sum of Powers of Norms 347\u003c\/p\u003e \u003cp\u003e10.2.6 Application of Ulam Stability Theory 348\u003c\/p\u003e \u003cp\u003e10.3 Various Forms of Functional Equations 348\u003c\/p\u003e \u003cp\u003e10.4 Preliminaries 353\u003c\/p\u003e \u003cp\u003e10.5 Rational Functional Equations 355\u003c\/p\u003e \u003cp\u003e10.5.1 Reciprocal Type Functional Equation 355\u003c\/p\u003e \u003cp\u003e10.5.2 Solution of Reciprocal Type Functional Equation 356\u003c\/p\u003e \u003cp\u003e10.5.3 Generalized Hyers–Ulam Stability of Reciprocal Type Functional Equation 357\u003c\/p\u003e \u003cp\u003e10.5.4 Counter-Example 360\u003c\/p\u003e \u003cp\u003e10.5.5 Geometrical Interpretation of Reciprocal Type Functional Equation 362\u003c\/p\u003e \u003cp\u003e10.5.6 An Application of Equation (10.41) to Electric Circuits 364\u003c\/p\u003e \u003cp\u003e10.5.7 Reciprocal-Quadratic Functional Equation 364\u003c\/p\u003e \u003cp\u003e10.5.8 General Solution of Reciprocal-Quadratic Functional Equation 366\u003c\/p\u003e \u003cp\u003e10.5.9 Generalized Hyers–Ulam Stability of Reciprocal-Quadratic Functional Equations 368\u003c\/p\u003e \u003cp\u003e10.5.10 Counter-Examples 373\u003c\/p\u003e \u003cp\u003e10.5.11 Reciprocal-Cubic and Reciprocal-Quartic Functional Equations 375\u003c\/p\u003e \u003cp\u003e10.5.12 Hyers–Ulam Stability of Reciprocal-Cubic and Reciprocal-Quartic Functional Equations 375\u003c\/p\u003e \u003cp\u003e10.5.13 Counter-Examples 380\u003c\/p\u003e \u003cp\u003e10.6 Euler-Lagrange–Jensen (\u003ci\u003ea, b; k = a + b\u003c\/i\u003e)-Sextic Functional Equations 384\u003c\/p\u003e \u003cp\u003e10.6.1 Generalized Ulam–Hyers Stability of Euler-Lagrange-Jensen Sextic Functional Equation Using Fixed Point Method 384\u003c\/p\u003e \u003cp\u003e10.6.2 Counter-Example 387\u003c\/p\u003e \u003cp\u003e10.6.3 Generalized Ulam–Hyers Stability of Euler-Lagrange-Jensen Sextic Functional Equation Using Direct Method 389\u003c\/p\u003e \u003cp\u003eReferences 395\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Attractor of the Generalized Contractive Iterated Function System 401\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMujahid Abbas and Talat Nazir\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Iterated Function System 401\u003c\/p\u003e \u003cp\u003e11.2 Generalized \u003ci\u003eF\u003c\/i\u003e-contractive Iterated Function System 407\u003c\/p\u003e \u003cp\u003e11.3 Iterated Function System in \u003ci\u003eb\u003c\/i\u003e-Metric Space 414\u003c\/p\u003e \u003cp\u003e11.4 Generalized \u003ci\u003eF\u003c\/i\u003e-Contractive Iterated Function System in b-Metric Space 420\u003c\/p\u003e \u003cp\u003eReferences 426\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Regular and Rapid Variations and Some Applications 429\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eLjubiša D.R. Kočinac, Dragan Djurčić, and Jelena V. Manojlović\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction and Historical Background 429\u003c\/p\u003e \u003cp\u003e12.2 Regular Variation 431\u003c\/p\u003e \u003cp\u003e12.2.1 The Class Tr(RV\u003csub\u003es\u003c\/sub\u003e) 432\u003c\/p\u003e \u003cp\u003e12.2.2 Classes of Sequences Related to Tr(RV\u003csub\u003es\u003c\/sub\u003e) 434\u003c\/p\u003e \u003cp\u003e12.2.3 The Class ORV\u003csub\u003es\u003c\/sub\u003e and Seneta Sequences 436\u003c\/p\u003e \u003cp\u003e12.3 Rapid Variation 437\u003c\/p\u003e \u003cp\u003e12.3.1 Some Properties of Rapidly Varying Functions 438\u003c\/p\u003e \u003cp\u003e12.3.2 The Class ARV\u003csub\u003es\u003c\/sub\u003e 440\u003c\/p\u003e \u003cp\u003e12.3.3 The Class KR\u003csub\u003es,∞\u003c\/sub\u003e 442\u003c\/p\u003e \u003cp\u003e12.3.4 The Class Tr(R\u003csub\u003es,∞\u003c\/sub\u003e) 447\u003c\/p\u003e \u003cp\u003e12.3.5 Subclasses of Tr(R\u003csub\u003es,∞\u003c\/sub\u003e) 448\u003c\/p\u003e \u003cp\u003e12.3.6 The Class Γ\u003csub\u003es\u003c\/sub\u003e 451\u003c\/p\u003e \u003cp\u003e12.4 Applications to Selection Principles 453\u003c\/p\u003e \u003cp\u003e12.4.1 First Results 455\u003c\/p\u003e \u003cp\u003e12.4.2 Improvements 455\u003c\/p\u003e \u003cp\u003e12.4.3 When ONE has a Winning Strategy? 460\u003c\/p\u003e \u003cp\u003e12.5 Applications to Differential Equations 463\u003c\/p\u003e \u003cp\u003e12.5.1 The Existence of all Solutions of (A) 464\u003c\/p\u003e \u003cp\u003e12.5.2 Superlinear Thomas–Fermi Equation (A) 466\u003c\/p\u003e \u003cp\u003e12.5.3 Sublinear Thomas–Fermi Equation (A) 470\u003c\/p\u003e \u003cp\u003e12.5.4 A Generalization 480\u003c\/p\u003e \u003cp\u003eReferences 486\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 \u003ci\u003en\u003c\/i\u003e-Inner Products, n-Norms, and Angles Between Two Subspaces 493\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eHendra Gunawan\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 493\u003c\/p\u003e \u003cp\u003e13.2 \u003ci\u003en\u003c\/i\u003e-Inner Product Spaces and n-Normed Spaces 495\u003c\/p\u003e \u003cp\u003e13.2.1 Topology in \u003ci\u003en\u003c\/i\u003e-Normed Spaces 499\u003c\/p\u003e \u003cp\u003e13.3 Orthogonality in \u003ci\u003en\u003c\/i\u003e-Normed Spaces 500\u003c\/p\u003e \u003cp\u003e13.3.1 \u003ci\u003eG-, P-, I-, \u003c\/i\u003eand\u003ci\u003e BJ-\u003c\/i\u003e Orthogonality 503\u003c\/p\u003e \u003cp\u003e13.3.2 Remarks on the \u003ci\u003en\u003c\/i\u003e-Dimensional Case 505\u003c\/p\u003e \u003cp\u003e13.4 Angles Between Two Subspaces 505\u003c\/p\u003e \u003cp\u003e13.4.1 An Explicit Formula 509\u003c\/p\u003e \u003cp\u003e13.4.2 A More General Formula 511\u003c\/p\u003e \u003cp\u003eReferences 513\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Proximal Fiber Bundles on Nerve Complexes 517\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJames F. Peters\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Brief Introduction 517\u003c\/p\u003e \u003cp\u003e14.2 Preliminaries 518\u003c\/p\u003e \u003cp\u003e14.2.1 Nerve Complexes and Nerve Spokes 518\u003c\/p\u003e \u003cp\u003e14.2.2 Descriptions and Proximities 521\u003c\/p\u003e \u003cp\u003e14.2.3 Descriptive Proximities 523\u003c\/p\u003e \u003cp\u003e14.3 Sewing Regions Together 527\u003c\/p\u003e \u003cp\u003e14.3.1 Sewing Nerves Together with Spokes to Construct a Nervous System Complex 529\u003c\/p\u003e \u003cp\u003e14.4 Some Results for Fiber Bundles 530\u003c\/p\u003e \u003cp\u003e14.5 Concluding Remarks 534\u003c\/p\u003e \u003cp\u003eReferences 534\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Approximation by Generalizations of Hybrid Baskakov Type Operators Preserving Exponential Functions 537\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eVijay Gupta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 537\u003c\/p\u003e \u003cp\u003e15.2 Baskakov–Szász Operators 539\u003c\/p\u003e \u003cp\u003e15.3 Genuine Baskakov–Szász Operators 542\u003c\/p\u003e \u003cp\u003e15.4 Preservation of e\u003csup\u003eAx\u003c\/sup\u003e 545\u003c\/p\u003e \u003cp\u003e15.5 Conclusion 549\u003c\/p\u003e \u003cp\u003eReferences 550\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Well-Posed Minimization Problems via the Theory of Measures of Noncompactness 553\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJózef Banaś and Tomasz Zając\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 553\u003c\/p\u003e \u003cp\u003e16.2 Minimization Problems and Their Well-Posedness in the Classical Sense 554\u003c\/p\u003e \u003cp\u003e16.3 Measures of Noncompactness 556\u003c\/p\u003e \u003cp\u003e16.4 Well-Posed Minimization Problems with Respect to Measures of Noncompactness 565\u003c\/p\u003e \u003cp\u003e16.5 Minimization Problems for Functionals Defined in Banach Sequence Spaces 568\u003c\/p\u003e \u003cp\u003e16.6 Minimization Problems for Functionals Defined in the Classical Space C([\u003ci\u003ea, b\u003c\/i\u003e])) 576\u003c\/p\u003e \u003cp\u003e16.7 Minimization Problems for Functionals Defined in the Space of Functions Continuous and Bounded on the Real Half-Axis 580\u003c\/p\u003e \u003cp\u003eReferences 584\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Some Recent Developments on Fixed Point Theory in Generalized Metric Spaces 587\u003cbr\u003e\u003c\/b\u003e\u003ci\u003ePoom Kumam and Somayya Komal\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Brief Introduction 587\u003c\/p\u003e \u003cp\u003e17.2 Some Basic Notions and Notations 593\u003c\/p\u003e \u003cp\u003e17.3 Fixed Points Theorems 596\u003c\/p\u003e \u003cp\u003e17.3.1 Fixed Points Theorems for Monotonic and Nonmonotonic Mappings 597\u003c\/p\u003e \u003cp\u003e17.3.2 PPF-Dependent Fixed-Point Theorems 600\u003c\/p\u003e \u003cp\u003e17.3.3 Fixed Points Results in b-Metric Spaces 602\u003c\/p\u003e \u003cp\u003e17.3.4 The generalized Ulam–Hyers Stability in \u003ci\u003eb\u003c\/i\u003e-Metric Spaces 604\u003c\/p\u003e \u003cp\u003e17.3.5 Well-Posedness of a Function with Respect to 𝛼-Admissibility in \u003ci\u003eb\u003c\/i\u003e-Metric Spaces 605\u003c\/p\u003e \u003cp\u003e17.3.6 Fixed Points for \u003ci\u003eF\u003c\/i\u003e-Contraction 606\u003c\/p\u003e \u003cp\u003e17.4 Common Fixed Points Theorems 608\u003c\/p\u003e \u003cp\u003e17.4.1 Common Fixed-Point Theorems for Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces 609\u003c\/p\u003e \u003cp\u003e17.5 Best Proximity Points 611\u003c\/p\u003e \u003cp\u003e17.6 Common Best Proximity Points 614\u003c\/p\u003e \u003cp\u003e17.7 Tripled Best Proximity Points 617\u003c\/p\u003e \u003cp\u003e17.8 Future Works 624\u003c\/p\u003e \u003cp\u003eReferences 624\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 The Basel Problem with an Extension 631\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAnthony Sofo\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 The Basel Problem 631\u003c\/p\u003e \u003cp\u003e18.2 An Euler Type Sum 640\u003c\/p\u003e \u003cp\u003e18.3 The Main Theorem 645\u003c\/p\u003e \u003cp\u003e18.4 Conclusion 652\u003c\/p\u003e \u003cp\u003eReferences 652\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Coupled Fixed Points and Coupled Coincidence Points via Fixed Point Theory 661\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAdrian Petruşel and Gabriela Petruşel\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction and Preliminaries 661\u003c\/p\u003e \u003cp\u003e19.2 Fixed Point Results 665\u003c\/p\u003e \u003cp\u003e19.2.1 The Single-Valued Case 665\u003c\/p\u003e \u003cp\u003e19.2.2 The Multi-Valued Case 673\u003c\/p\u003e \u003cp\u003e19.3 Coupled Fixed Point Results 680\u003c\/p\u003e \u003cp\u003e19.3.1 The Single-Valued Case 680\u003c\/p\u003e \u003cp\u003e19.3.2 The Multi-Valued Case 686\u003c\/p\u003e \u003cp\u003e19.4 Coincidence Point Results 689\u003c\/p\u003e \u003cp\u003e19.5 Coupled Coincidence Results 699\u003c\/p\u003e \u003cp\u003eReferences 704\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 The Corona Problem, Carleson Measures, and Applications 709\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAlberto Saracco\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 The Corona Problem 709\u003c\/p\u003e \u003cp\u003e20.1.1 Banach Algebras: Spectrum 709\u003c\/p\u003e \u003cp\u003e20.1.2 Banach Algebras: Maximal Spectrum 710\u003c\/p\u003e \u003cp\u003e20.1.3 The Algebra of Bounded Holomorphic Functions and the Corona Problem 710\u003c\/p\u003e \u003cp\u003e20.2 Carleson’s Proof and Carleson Measures 711\u003c\/p\u003e \u003cp\u003e20.2.1 Wolff’s Proof 712\u003c\/p\u003e \u003cp\u003e20.3 The Corona Problem in Higher Henerality 712\u003c\/p\u003e \u003cp\u003e20.3.1 The Corona Problem in ℂ 712\u003c\/p\u003e \u003cp\u003e20.3.2 The Corona Problem in Riemann Surfaces: A Positive and a Negative Result 713\u003c\/p\u003e \u003cp\u003e20.3.3 The Corona Problem in Domains of ℂ\u003csup\u003en\u003c\/sup\u003e 714\u003c\/p\u003e \u003cp\u003e20.3.4 The Corona Problem for Quaternionic Slice-Regular Functions 715\u003c\/p\u003e \u003cp\u003e20.3.4.1 Slice-Regular Functions \u003ci\u003ef\u003c\/i\u003e ∶ \u003ci\u003eD\u003c\/i\u003e → ℍ 715\u003c\/p\u003e \u003cp\u003e20.3.4.2 The Corona Theorem in the Quaternions 717\u003c\/p\u003e \u003cp\u003e20.4 Results on Carleson Measures 718\u003c\/p\u003e \u003cp\u003e20.4.1 Carleson Measures of Hardy Spaces of the Disk 718\u003c\/p\u003e \u003cp\u003e20.4.2 Carleson Measures of Bergman Spaces of the Disk 719\u003c\/p\u003e \u003cp\u003e20.4.3 Carleson Measures in the Unit Ball of ℂ\u003csup\u003en\u003c\/sup\u003e 720\u003c\/p\u003e \u003cp\u003e20.4.4 Carleson Measures in Strongly Pseudoconvex Bounded Domains of ℂ\u003csup\u003en\u003c\/sup\u003e 722\u003c\/p\u003e \u003cp\u003e20.4.5 Generalizations of Carleson Measures and Applications to Toeplitz Operators 723\u003c\/p\u003e \u003cp\u003e20.4.6 Explicit Examples of Carleson Measures of Bergman Spaces 724\u003c\/p\u003e \u003cp\u003e20.4.7 Carleson Measures in the Quaternionic Setting 725\u003c\/p\u003e \u003cp\u003e20.4.7.1 Carleson Measures on Hardy Spaces of 𝔹 ⊂ ℍ 725\u003c\/p\u003e \u003cp\u003e20.4.7.2 Carleson Measures on Bergman Spaces of 𝔹 ⊂ ℍ 726\u003c\/p\u003e \u003cp\u003eReferences 728\u003c\/p\u003e \u003cp\u003eIndex 731\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407048745303,"sku":"9781119414346","price":105.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119414346.jpg?v=1730497999"},{"product_id":"precalculus-for-dummies-9781119508779","title":"PreCalculus For Dummies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eIntroduction\u003c\/b\u003e\u003cb\u003e 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAbout This Book 1\u003c\/p\u003e \u003cp\u003eFoolish Assumptions 2\u003c\/p\u003e \u003cp\u003eIcons Used in This Book 3\u003c\/p\u003e \u003cp\u003eBeyond the Book 3\u003c\/p\u003e \u003cp\u003eWhere to Go from Here 3\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 1: Getting Started with Pre-Calculus\u003c\/b\u003e\u003cb\u003e 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1: Pre-Pre-Calculus\u003c\/b\u003e\u003cb\u003e 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePre-Calculus: An Overview 8\u003c\/p\u003e \u003cp\u003eAll the Number Basics (No, Not How to Count Them!) 9\u003c\/p\u003e \u003cp\u003eThe multitude of number types: Terms to know 9\u003c\/p\u003e \u003cp\u003eThe fundamental operations you can perform on numbers 11\u003c\/p\u003e \u003cp\u003eThe properties of numbers: Truths to remember 11\u003c\/p\u003e \u003cp\u003eVisual Statements: When Math Follows Form with Function 12\u003c\/p\u003e \u003cp\u003eBasic terms and concepts 13\u003c\/p\u003e \u003cp\u003eGraphing linear equalities and inequalities 14\u003c\/p\u003e \u003cp\u003eGathering information from graphs 15\u003c\/p\u003e \u003cp\u003eGet Yourself a Graphing Calculator 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2: Playing with Real Numbers\u003c\/b\u003e\u003cb\u003e 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSolving Inequalities 19\u003c\/p\u003e \u003cp\u003eRecapping inequality how-tos 20\u003c\/p\u003e \u003cp\u003eSolving equations and inequalities when absolute value is involved 20\u003c\/p\u003e \u003cp\u003eExpressing solutions for inequalities with interval notation 22\u003c\/p\u003e \u003cp\u003eVariations on Dividing and Multiplying: Working with Radicals and Exponents 24\u003c\/p\u003e \u003cp\u003eDefining and relating radicals and exponents 24\u003c\/p\u003e \u003cp\u003eRewriting radicals as exponents (or, creating rational exponents) 25\u003c\/p\u003e \u003cp\u003eGetting a radical out of a denominator: Rationalizing 26\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3: The Building Blocks of Pre-Calculus Functions\u003c\/b\u003e\u003cb\u003e 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eQualities of Special Function Types and Their Graphs 32\u003c\/p\u003e \u003cp\u003eEven and odd functions 32\u003c\/p\u003e \u003cp\u003eOne-to-one functions 32\u003c\/p\u003e \u003cp\u003eDealing with Parent Functions and Their Graphs 33\u003c\/p\u003e \u003cp\u003eLinear functions 33\u003c\/p\u003e \u003cp\u003eQuadratic functions 33\u003c\/p\u003e \u003cp\u003eSquare-root functions 34\u003c\/p\u003e \u003cp\u003eAbsolute-value functions 34\u003c\/p\u003e \u003cp\u003eCubic functions 35\u003c\/p\u003e \u003cp\u003eCube-root functions 36\u003c\/p\u003e \u003cp\u003eGraphing Functions That Have More Than One Rule: Piece-Wise Functions 37\u003c\/p\u003e \u003cp\u003eSetting the Stage for Rational Functions 38\u003c\/p\u003e \u003cp\u003eStep 1: Search for vertical asymptotes 39\u003c\/p\u003e \u003cp\u003eStep 2: Look for horizontal asymptotes 40\u003c\/p\u003e \u003cp\u003eStep 3: Seek out oblique asymptotes 41\u003c\/p\u003e \u003cp\u003eStep 4: Locate the x- and y-intercepts 42\u003c\/p\u003e \u003cp\u003ePutting the Results to Work: Graphing Rational Functions 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4: Operating on Functions\u003c\/b\u003e\u003cb\u003e 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eTransforming the Parent Graphs 50\u003c\/p\u003e \u003cp\u003eStretching and flattening 50\u003c\/p\u003e \u003cp\u003eTranslations 52\u003c\/p\u003e \u003cp\u003eReflections 54\u003c\/p\u003e \u003cp\u003eCombining various transformations (a transformation in itself!) 55\u003c\/p\u003e \u003cp\u003eTransforming functions point by point 57\u003c\/p\u003e \u003cp\u003eSharpen Your Scalpel: Operating on Functions 58\u003c\/p\u003e \u003cp\u003eAdding and subtracting 59\u003c\/p\u003e \u003cp\u003eMultiplying and dividing 60\u003c\/p\u003e \u003cp\u003eBreaking down a composition of functions 60\u003c\/p\u003e \u003cp\u003eAdjusting the domain and range of combined functions (if applicable) 61\u003c\/p\u003e \u003cp\u003eTurning Inside Out with Inverse Functions 63\u003c\/p\u003e \u003cp\u003eGraphing an inverse 64\u003c\/p\u003e \u003cp\u003eInverting a function to find its inverse 66\u003c\/p\u003e \u003cp\u003eVerifying an inverse 66\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5: Digging Out and Using Roots to Graph Polynomial Functions\u003c\/b\u003e\u003cb\u003e 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Degrees and Roots 70\u003c\/p\u003e \u003cp\u003eFactoring a Polynomial Expression 71\u003c\/p\u003e \u003cp\u003eAlways the first step: Looking for a GCF 72\u003c\/p\u003e \u003cp\u003eUnwrapping the box containing a trinomial 73\u003c\/p\u003e \u003cp\u003eRecognizing and factoring special polynomials 74\u003c\/p\u003e \u003cp\u003eGrouping to factor four or more terms 77\u003c\/p\u003e \u003cp\u003eFinding the Roots of a Factored Equation 78\u003c\/p\u003e \u003cp\u003eCracking a Quadratic Equation When It Won’t Factor 79\u003c\/p\u003e \u003cp\u003eUsing the quadratic formula 79\u003c\/p\u003e \u003cp\u003eCompleting the square 80\u003c\/p\u003e \u003cp\u003eSolving Unfactorable Polynomials with a Degree Higher Than Two 81\u003c\/p\u003e \u003cp\u003eCounting a polynomial’s total roots 82\u003c\/p\u003e \u003cp\u003eTallying the real roots: Descartes’s rule of signs 82\u003c\/p\u003e \u003cp\u003eAccounting for imaginary roots: The fundamental theorem of algebra 83\u003c\/p\u003e \u003cp\u003eGuessing and checking the real roots 84\u003c\/p\u003e \u003cp\u003ePut It in Reverse: Using Solutions to Find Factors 90\u003c\/p\u003e \u003cp\u003eGraphing Polynomials 91\u003c\/p\u003e \u003cp\u003eWhen all the roots are real numbers 91\u003c\/p\u003e \u003cp\u003eWhen roots are imaginary numbers: Combining all techniques 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6: Exponential and Logarithmic Functions\u003c\/b\u003e\u003cb\u003e 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eExploring Exponential Functions 98\u003c\/p\u003e \u003cp\u003eSearching the ins and outs of exponential functions 98\u003c\/p\u003e \u003cp\u003eGraphing and transforming exponential functions 100\u003c\/p\u003e \u003cp\u003eLogarithms: The Inverse of Exponential Functions 102\u003c\/p\u003e \u003cp\u003eGetting a better handle on logarithms 102\u003c\/p\u003e \u003cp\u003eManaging the properties and identities of logs 103\u003c\/p\u003e \u003cp\u003eChanging a log’s base 105\u003c\/p\u003e \u003cp\u003eCalculating a number when you know its log: Inverse logs 105\u003c\/p\u003e \u003cp\u003eGraphing logs 106\u003c\/p\u003e \u003cp\u003eBase Jumping to Simplify and Solve Equations 109\u003c\/p\u003e \u003cp\u003eStepping through the process of exponential equation solving 109\u003c\/p\u003e \u003cp\u003eSolving logarithmic equations 112\u003c\/p\u003e \u003cp\u003eGrowing Exponentially: Word Problems in the Kitchen 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 2: The Essentials of Trigonometry\u003c\/b\u003e\u003cb\u003e 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7: Circling in on Angles\u003c\/b\u003e\u003cb\u003e 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroducing Radians: Circles Weren’t Always Measured in Degrees 120\u003c\/p\u003e \u003cp\u003eTrig Ratios: Taking Right Triangles a Step Further 121\u003c\/p\u003e \u003cp\u003eMaking a sine 121\u003c\/p\u003e \u003cp\u003eLooking for a cosine 122\u003c\/p\u003e \u003cp\u003eGoing on a tangent 124\u003c\/p\u003e \u003cp\u003eDiscovering the flip side: Reciprocal trig functions 125\u003c\/p\u003e \u003cp\u003eWorking in reverse: Inverse trig functions 126\u003c\/p\u003e \u003cp\u003eUnderstanding How Trig Ratios Work on the Coordinate Plane 127\u003c\/p\u003e \u003cp\u003eBuilding the Unit Circle by Dissecting the Right Way 129\u003c\/p\u003e \u003cp\u003eFamiliarizing yourself with the most common angles 129\u003c\/p\u003e \u003cp\u003eDrawing uncommon angles 131\u003c\/p\u003e \u003cp\u003eDigesting Special Triangle Ratios 132\u003c\/p\u003e \u003cp\u003eThe 45er: 45 -45 -90 triangle 132\u003c\/p\u003e \u003cp\u003eThe old 30-60: 30 -60 -90 triangle 133\u003c\/p\u003e \u003cp\u003eTriangles and the Unit Circle: Working Together for the Common Good 135\u003c\/p\u003e \u003cp\u003ePlacing the major angles correctly, sans protractor 135\u003c\/p\u003e \u003cp\u003eRetrieving trig-function values on the unit circle 138\u003c\/p\u003e \u003cp\u003eFinding the reference angle to solve for angles on the unit circle 142\u003c\/p\u003e \u003cp\u003eMeasuring Arcs: When the Circle Is Put in Motion 146\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8: Simplifying the Graphing and Transformation of Trig Functions\u003c\/b\u003e\u003cb\u003e 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDrafting the Sine and Cosine Parent Graphs 150\u003c\/p\u003e \u003cp\u003eSketching sine 150\u003c\/p\u003e \u003cp\u003eLooking at cosine 152\u003c\/p\u003e \u003cp\u003eGraphing Tangent and Cotangent 154\u003c\/p\u003e \u003cp\u003eTackling tangent 154\u003c\/p\u003e \u003cp\u003eClarifying cotangent 157\u003c\/p\u003e \u003cp\u003ePutting Secant and Cosecant in Pictures 159\u003c\/p\u003e \u003cp\u003eGraphing secant 159\u003c\/p\u003e \u003cp\u003eChecking out cosecant 161\u003c\/p\u003e \u003cp\u003eTransforming Trig Graphs 162\u003c\/p\u003e \u003cp\u003eMessing with sine and cosine graphs 163\u003c\/p\u003e \u003cp\u003eTweaking tangent and cotangent graphs 173\u003c\/p\u003e \u003cp\u003eTransforming the graphs of secant and cosecant 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9: Identifying with Trig Identities: The Basics\u003c\/b\u003e\u003cb\u003e 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eKeeping the End in Mind: A Quick Primer on Identities 182\u003c\/p\u003e \u003cp\u003eLining Up the Means to the End: Basic Trig Identities 182\u003c\/p\u003e \u003cp\u003eReciprocal and ratio identities 183\u003c\/p\u003e \u003cp\u003ePythagorean identities 185\u003c\/p\u003e \u003cp\u003eEven\/odd identities 188\u003c\/p\u003e \u003cp\u003eCo-function identities 190\u003c\/p\u003e \u003cp\u003ePeriodicity identities 192\u003c\/p\u003e \u003cp\u003eTackling Difficult Trig Proofs: Some Techniques to Know 194\u003c\/p\u003e \u003cp\u003eDealing with demanding denominators 195\u003c\/p\u003e \u003cp\u003eGoing solo on each side 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10: Advanced Identities: Your Keys to Success\u003c\/b\u003e\u003cb\u003e 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFinding Trig Functions of Sums and Differences 202\u003c\/p\u003e \u003cp\u003eSearching out the sine of \u003ci\u003ea b \u003c\/i\u003e202\u003c\/p\u003e \u003cp\u003eCalculating the cosine of \u003ci\u003ea b \u003c\/i\u003e206\u003c\/p\u003e \u003cp\u003eTaming the tangent of \u003ci\u003ea b \u003c\/i\u003e209\u003c\/p\u003e \u003cp\u003eDoubling an Angle and Finding Its Trig Value 211\u003c\/p\u003e \u003cp\u003eFinding the sine of a doubled angle 212\u003c\/p\u003e \u003cp\u003eCalculating cosines for two 213\u003c\/p\u003e \u003cp\u003eSquaring your cares away 215\u003c\/p\u003e \u003cp\u003eHaving twice the fun with tangents 216\u003c\/p\u003e \u003cp\u003eTaking Trig Functions of Common Angles Divided in Two 217\u003c\/p\u003e \u003cp\u003eA Glimpse of Calculus: Traveling from Products to Sums and Back 219\u003c\/p\u003e \u003cp\u003eExpressing products as sums (or differences) 219\u003c\/p\u003e \u003cp\u003eTransporting from sums (or differences) to products 220\u003c\/p\u003e \u003cp\u003eEliminating Exponents with Power-Reducing Formulas 221\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11: Taking Charge of Oblique Triangles with the Laws of Sines and Cosines\u003c\/b\u003e\u003cb\u003e 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSolving a Triangle with the Law of Sines 224\u003c\/p\u003e \u003cp\u003eWhen you know two angle measures 225\u003c\/p\u003e \u003cp\u003eWhen you know two consecutive side lengths 228\u003c\/p\u003e \u003cp\u003eConquering a Triangle with the Law of Cosines 235\u003c\/p\u003e \u003cp\u003eSSS: Finding angles using only sides 236\u003c\/p\u003e \u003cp\u003eSAS: Tagging the angle in the middle (and the two sides) 238\u003c\/p\u003e \u003cp\u003eFilling in the Triangle by Calculating Area 240\u003c\/p\u003e \u003cp\u003eFinding area with two sides and an included angle (for SAS scenarios) 241\u003c\/p\u003e \u003cp\u003eUsing Heron’s Formula (for SSS scenarios) 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 3: Analytic Geometry and System Solving\u003c\/b\u003e\u003cb\u003e 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12: Plane Thinking: Complex Numbers and Polar Coordinates\u003c\/b\u003e\u003cb\u003e 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Real versus Imaginary 246\u003c\/p\u003e \u003cp\u003eCombining Real and Imaginary: The Complex Number System 247\u003c\/p\u003e \u003cp\u003eGrasping the usefulness of complex numbers 247\u003c\/p\u003e \u003cp\u003ePerforming operations with complex numbers 248\u003c\/p\u003e \u003cp\u003eGraphing Complex Numbers 250\u003c\/p\u003e \u003cp\u003ePlotting Around a Pole: Polar Coordinates 251\u003c\/p\u003e \u003cp\u003eWrapping your brain around the polar coordinate plane 252\u003c\/p\u003e \u003cp\u003eGraphing polar coordinates with negative values 254\u003c\/p\u003e \u003cp\u003eChanging to and from polar coordinates 256\u003c\/p\u003e \u003cp\u003ePicturing polar equations 259\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13: Creating Conics by Slicing Cones\u003c\/b\u003e\u003cb\u003e 263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCone to Cone: Identifying the Four Conic Sections 264\u003c\/p\u003e \u003cp\u003eIn picture (graph form) 264\u003c\/p\u003e \u003cp\u003eIn print (equation form) 266\u003c\/p\u003e \u003cp\u003eGoing Round and Round: Graphing Circles 267\u003c\/p\u003e \u003cp\u003eGraphing circles at the origin 267\u003c\/p\u003e \u003cp\u003eGraphing circles away from the origin 268\u003c\/p\u003e \u003cp\u003eWriting in center–radius form 269\u003c\/p\u003e \u003cp\u003eRiding the Ups and Downs with Parabolas 270\u003c\/p\u003e \u003cp\u003eLabeling the parts 270\u003c\/p\u003e \u003cp\u003eUnderstanding the characteristics of a standard parabola 271\u003c\/p\u003e \u003cp\u003ePlotting the variations: Parabolas all over the plane 272\u003c\/p\u003e \u003cp\u003eThe vertex, axis of symmetry, focus, and directrix 273\u003c\/p\u003e \u003cp\u003eIdentifying the min and max of vertical parabolas 276\u003c\/p\u003e \u003cp\u003eThe Fat and the Skinny on the Ellipse 278\u003c\/p\u003e \u003cp\u003eLabeling ellipses and expressing them with algebra 279\u003c\/p\u003e \u003cp\u003eIdentifying the parts from the equation 281\u003c\/p\u003e \u003cp\u003ePair Two Curves and What Do You Get? Hyperbolas 284\u003c\/p\u003e \u003cp\u003eVisualizing the two types of hyperbolas and their bits and pieces 284\u003c\/p\u003e \u003cp\u003eGraphing a hyperbola from an equation 287\u003c\/p\u003e \u003cp\u003eFinding the equations of asymptotes 287\u003c\/p\u003e \u003cp\u003eExpressing Conics Outside the Realm of Cartesian Coordinates 289\u003c\/p\u003e \u003cp\u003eGraphing conic sections in parametric form 290\u003c\/p\u003e \u003cp\u003eThe equations of conic sections on the polar coordinate plane 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14: Streamlining Systems, Managing Variables \u003c\/b\u003e\u003cb\u003e295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA Primer on Your System-Solving Options 296\u003c\/p\u003e \u003cp\u003eAlgebraic Solutions of Two-Equation Systems 297\u003c\/p\u003e \u003cp\u003eSolving linear systems 297\u003c\/p\u003e \u003cp\u003eWorking nonlinear systems 300\u003c\/p\u003e \u003cp\u003eSolving Systems with More than Two Equations 304\u003c\/p\u003e \u003cp\u003eDecomposing Partial Fractions 306\u003c\/p\u003e \u003cp\u003eSurveying Systems of Inequalities 307\u003c\/p\u003e \u003cp\u003eIntroducing Matrices: The Basics 309\u003c\/p\u003e \u003cp\u003eApplying basic operations to matrices 310\u003c\/p\u003e \u003cp\u003eMultiplying matrices by each other 311\u003c\/p\u003e \u003cp\u003eSimplifying Matrices to Ease the Solving Process 312\u003c\/p\u003e \u003cp\u003eWriting a system in matrix form 313\u003c\/p\u003e \u003cp\u003eReduced row-echelon form 313\u003c\/p\u003e \u003cp\u003eAugmented form 314\u003c\/p\u003e \u003cp\u003eMaking Matrices Work for You 315\u003c\/p\u003e \u003cp\u003eUsing Gaussian elimination to solve systems 316\u003c\/p\u003e \u003cp\u003eMultiplying a matrix by its inverse 320\u003c\/p\u003e \u003cp\u003eUsing determinants: Cramer’s Rule 323\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 15: Sequences, Series, and Expanding Binomials for the Real World\u003c\/b\u003e\u003cb\u003e 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSpeaking Sequentially: Grasping the General Method 328\u003c\/p\u003e \u003cp\u003eDetermining a sequence’s terms 328\u003c\/p\u003e \u003cp\u003eWorking in reverse: Forming an expression from terms 329\u003c\/p\u003e \u003cp\u003eRecursive sequences: One type of general sequence 330\u003c\/p\u003e \u003cp\u003eDifference between Terms: Arithmetic Sequences 331\u003c\/p\u003e \u003cp\u003eUsing consecutive terms to find another 332\u003c\/p\u003e \u003cp\u003eUsing any two terms 332\u003c\/p\u003e \u003cp\u003eRatios and Consecutive Paired Terms: Geometric Sequences 334\u003c\/p\u003e \u003cp\u003eIdentifying a particular term when given consecutive terms 334\u003c\/p\u003e \u003cp\u003eGoing out of order: Dealing with nonconsecutive terms 335\u003c\/p\u003e \u003cp\u003eCreating a Series: Summing Terms of a Sequence 337\u003c\/p\u003e \u003cp\u003eReviewing general summation notation 337\u003c\/p\u003e \u003cp\u003eSumming an arithmetic sequence 338\u003c\/p\u003e \u003cp\u003eSeeing how a geometric sequence adds up 339\u003c\/p\u003e \u003cp\u003eExpanding with the Binomial Theorem 342\u003c\/p\u003e \u003cp\u003eBreaking down the binomial theorem 344\u003c\/p\u003e \u003cp\u003eExpanding by using the binomial theorem 345\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 16: Onward to Calculus\u003c\/b\u003e\u003cb\u003e 351\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eScoping Out the Differences between Pre-Calculus and Calculus 352\u003c\/p\u003e \u003cp\u003eUnderstanding Your Limits 353\u003c\/p\u003e \u003cp\u003eFinding the Limit of a Function 355\u003c\/p\u003e \u003cp\u003eGraphically 355\u003c\/p\u003e \u003cp\u003eAnalytically 356\u003c\/p\u003e \u003cp\u003eAlgebraically 357\u003c\/p\u003e \u003cp\u003eOperating on Limits: The Limit Laws 361\u003c\/p\u003e \u003cp\u003eCalculating the Average Rate of Change 362\u003c\/p\u003e \u003cp\u003eExploring Continuity in Functions 363\u003c\/p\u003e \u003cp\u003eDetermining whether a function is continuous 364\u003c\/p\u003e \u003cp\u003eDiscontinuity in rational functions 365\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 4: The Part of Tens\u003c\/b\u003e\u003cb\u003e 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 17: Ten Polar Graphs \u003c\/b\u003e\u003cb\u003e369\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSpiraling Outward 369\u003c\/p\u003e \u003cp\u003eFalling in Love with a Cardioid 370\u003c\/p\u003e \u003cp\u003eCardioids and Lima Beans 370\u003c\/p\u003e \u003cp\u003eLeaning Lemniscates 371\u003c\/p\u003e \u003cp\u003eLacing through Lemniscates 372\u003c\/p\u003e \u003cp\u003eRoses with Even Petals 372\u003c\/p\u003e \u003cp\u003eA rose Is a Rose Is a Rose 373\u003c\/p\u003e \u003cp\u003eLimaçon or Escargot? 373\u003c\/p\u003e \u003cp\u003eLimaçon on the Side 374\u003c\/p\u003e \u003cp\u003eBifolium or Rabbit Ears? 374\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 18: Ten Habits to Adjust before Calculus\u003c\/b\u003e\u003cb\u003e 375\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFigure Out What the Problem Is Asking 375\u003c\/p\u003e \u003cp\u003eDraw Pictures (the More the Better) 376\u003c\/p\u003e \u003cp\u003ePlan Your Attack — Identify Your Targets 377\u003c\/p\u003e \u003cp\u003eWrite Down Any Formulas 377\u003c\/p\u003e \u003cp\u003eShow Each Step of Your Work 378\u003c\/p\u003e \u003cp\u003eKnow When to Quit 378\u003c\/p\u003e \u003cp\u003eCheck Your Answers 379\u003c\/p\u003e \u003cp\u003ePractice Plenty of Problems 380\u003c\/p\u003e \u003cp\u003eKeep Track of the Order of Operations 380\u003c\/p\u003e \u003cp\u003eUse Caution When Dealing with Fractions 381\u003c\/p\u003e \u003cp\u003eIndex 383\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407068373335,"sku":"9781119508779","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119508779.jpg?v=1730498064"},{"product_id":"calculus-essentials-for-dummies-9781119591207","title":"Calculus Essentials For Dummies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus Essentials For Dummies(9781119591207) was previously published asCalculus Essentials For Dummies (9780470618356). While this version features a newDummiescover and design, the content is the same as the prior release and should not be considered a new or updated product.     Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option.Calculus Essentials For Dummiesprovides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material,Calculus Essentials For Dummiessticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eIntroduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAbout This Book 1\u003c\/p\u003e \u003cp\u003eConventions Used in This Book 2\u003c\/p\u003e \u003cp\u003eFoolish Assumptions 2\u003c\/p\u003e \u003cp\u003eIcons Used in This Book 3\u003c\/p\u003e \u003cp\u003eWhere to Go from Here 3\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1: Calculus: No Big Deal\u003c\/b\u003e\u003cb\u003e 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSo What is Calculus Already? 5\u003c\/p\u003e \u003cp\u003eReal-World Examples of Calculus 7\u003c\/p\u003e \u003cp\u003eDifferentiation 8\u003c\/p\u003e \u003cp\u003eIntegration 9\u003c\/p\u003e \u003cp\u003eWhy Calculus Works 11\u003c\/p\u003e \u003cp\u003eLimits: Math microscopes 11\u003c\/p\u003e \u003cp\u003eWhat happens when you zoom in 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2: Limits and Continuity\u003c\/b\u003e\u003cb\u003e 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eTaking it to the Limit 15\u003c\/p\u003e \u003cp\u003eThree functions with one limit 15\u003c\/p\u003e \u003cp\u003eOne-sided limits 17\u003c\/p\u003e \u003cp\u003eLimits and vertical asymptotes 18\u003c\/p\u003e \u003cp\u003eLimits and horizontal asymptotes 18\u003c\/p\u003e \u003cp\u003eInstantaneous speed 19\u003c\/p\u003e \u003cp\u003eLimits and Continuity 21\u003c\/p\u003e \u003cp\u003eThe hole exception 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3: Evaluating Limits\u003c\/b\u003e\u003cb\u003e 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eEasy Limits 25\u003c\/p\u003e \u003cp\u003eLimits to memorize 25\u003c\/p\u003e \u003cp\u003ePlug-and-chug limits 26\u003c\/p\u003e \u003cp\u003e“Real” Limit Problems 26\u003c\/p\u003e \u003cp\u003eFactoring 27\u003c\/p\u003e \u003cp\u003eConjugate multiplication 27\u003c\/p\u003e \u003cp\u003eMiscellaneous algebra 28\u003c\/p\u003e \u003cp\u003eLimits at Infinity 29\u003c\/p\u003e \u003cp\u003eHorizontal asymptotes 30\u003c\/p\u003e \u003cp\u003eSolving limits at infinity 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4: Differentiation Orientation\u003c\/b\u003e\u003cb\u003e 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Derivative: It’s Just Slope 34\u003c\/p\u003e \u003cp\u003eThe slope of a line 35\u003c\/p\u003e \u003cp\u003eThe derivative of a line 36\u003c\/p\u003e \u003cp\u003eThe Derivative: It’s Just a Rate 36\u003c\/p\u003e \u003cp\u003eCalculus on the playground 36\u003c\/p\u003e \u003cp\u003eThe rate-slope connection 38\u003c\/p\u003e \u003cp\u003eThe Derivative of a Curve 39\u003c\/p\u003e \u003cp\u003eThe Difference Quotient 40\u003c\/p\u003e \u003cp\u003eAverage and Instantaneous Rate 46\u003c\/p\u003e \u003cp\u003eThree Cases Where the Derivative Does Not Exist 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5: Differentiation Rules\u003c\/b\u003e\u003cb\u003e 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBasic Differentiation Rules 49\u003c\/p\u003e \u003cp\u003eThe constant rule 49\u003c\/p\u003e \u003cp\u003eThe power rule 49\u003c\/p\u003e \u003cp\u003eThe constant multiple rule 50\u003c\/p\u003e \u003cp\u003eThe sum and difference rules 51\u003c\/p\u003e \u003cp\u003eDifferentiating trig functions 52\u003c\/p\u003e \u003cp\u003eExponential and logarithmic functions 52\u003c\/p\u003e \u003cp\u003eDerivative Rules for Experts 53\u003c\/p\u003e \u003cp\u003eThe product and quotient rules 53\u003c\/p\u003e \u003cp\u003eThe chain rule 54\u003c\/p\u003e \u003cp\u003eDifferentiating Implicitly 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6: Differentiation and the Shape of Curves\u003c\/b\u003e\u003cb\u003e 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA Calculus Road Trip 61\u003c\/p\u003e \u003cp\u003eLocal Extrema 63\u003c\/p\u003e \u003cp\u003eFinding the critical numbers 63\u003c\/p\u003e \u003cp\u003eThe First Derivative Test 65\u003c\/p\u003e \u003cp\u003eThe Second Derivative Test 66\u003c\/p\u003e \u003cp\u003eFinding Absolute Extrema on a Closed Interval 69\u003c\/p\u003e \u003cp\u003eFinding Absolute Extrema over a Function’s Entire Domain 71\u003c\/p\u003e \u003cp\u003eConcavity and Inflection Points 73\u003c\/p\u003e \u003cp\u003eGraphs of Derivatives 75\u003c\/p\u003e \u003cp\u003eThe Mean Value Theorem 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7: Differentiation Problems\u003c\/b\u003e\u003cb\u003e 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOptimization Problems 81\u003c\/p\u003e \u003cp\u003eThe maximum area of a corral 81\u003c\/p\u003e \u003cp\u003ePosition, Velocity, and Acceleration 83\u003c\/p\u003e \u003cp\u003eVelocity versus speed 84\u003c\/p\u003e \u003cp\u003eMaximum and minimum height 86\u003c\/p\u003e \u003cp\u003eVelocity and displacement 87\u003c\/p\u003e \u003cp\u003eSpeed and distance travelled 88\u003c\/p\u003e \u003cp\u003eAcceleration 89\u003c\/p\u003e \u003cp\u003eTying it all together 90\u003c\/p\u003e \u003cp\u003eRelated Rates 91\u003c\/p\u003e \u003cp\u003eA calculus crossroads 91\u003c\/p\u003e \u003cp\u003eFilling up a trough 94\u003c\/p\u003e \u003cp\u003eLinear Approximation 97\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8: Introduction to Integration \u003c\/b\u003e\u003cb\u003e101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntegration: Just Fancy Addition 101\u003c\/p\u003e \u003cp\u003eFinding the Area under a Curve 103\u003c\/p\u003e \u003cp\u003eDealing with negative area 105\u003c\/p\u003e \u003cp\u003eApproximating Area 105\u003c\/p\u003e \u003cp\u003eApproximating area with left sums 105\u003c\/p\u003e \u003cp\u003eApproximating area with right sums 108\u003c\/p\u003e \u003cp\u003eApproximating area with midpoint sums 110\u003c\/p\u003e \u003cp\u003eSummation Notation 112\u003c\/p\u003e \u003cp\u003eSumming up the basics 112\u003c\/p\u003e \u003cp\u003eWriting Riemann sums with sigma notation 113\u003c\/p\u003e \u003cp\u003eFinding Exact Area with the Definite Integral 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9: Integration: Backwards Differentiation \u003c\/b\u003e\u003cb\u003e119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAntidifferentiation: Reverse Differentiation 119\u003c\/p\u003e \u003cp\u003eThe Annoying Area Function 121\u003c\/p\u003e \u003cp\u003eThe Fundamental Theorem 124\u003c\/p\u003e \u003cp\u003eFundamental Theorem: Take Two 126\u003c\/p\u003e \u003cp\u003eAntiderivatives: Basic Techniques 128\u003c\/p\u003e \u003cp\u003eReverse rules 128\u003c\/p\u003e \u003cp\u003eGuess and check 130\u003c\/p\u003e \u003cp\u003eSubstitution 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10: Integration for Experts \u003c\/b\u003e\u003cb\u003e137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntegration by Parts 137\u003c\/p\u003e \u003cp\u003ePicking your u 139\u003c\/p\u003e \u003cp\u003eTricky Trig Integrals 141\u003c\/p\u003e \u003cp\u003eSines and cosines 141\u003c\/p\u003e \u003cp\u003eSecants and tangents 144\u003c\/p\u003e \u003cp\u003eCosecants and cotangents 147\u003c\/p\u003e \u003cp\u003eTrigonometric Substitution 147\u003c\/p\u003e \u003cp\u003eCase 1: Tangents 148\u003c\/p\u003e \u003cp\u003eCase 2: Sines 150\u003c\/p\u003e \u003cp\u003eCase 3: Secants 151\u003c\/p\u003e \u003cp\u003ePartial Fractions 152\u003c\/p\u003e \u003cp\u003eCase 1: The denominator contains only linear factors 152\u003c\/p\u003e \u003cp\u003eCase 2: The denominator contains unfactorable quadratic factors 153\u003c\/p\u003e \u003cp\u003eCase 3: The denominator contains repeated factors 155\u003c\/p\u003e \u003cp\u003eEquating coefficients 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11: Using the Integral to Solve Problems\u003c\/b\u003e\u003cb\u003e 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Mean Value Theorem for Integrals and Average Value 158\u003c\/p\u003e \u003cp\u003eThe Area between Two Curves 160\u003c\/p\u003e \u003cp\u003eVolumes of Weird Solids 162\u003c\/p\u003e \u003cp\u003eThe meat-slicer method 162\u003c\/p\u003e \u003cp\u003eThe disk method 163\u003c\/p\u003e \u003cp\u003eThe washer method 165\u003c\/p\u003e \u003cp\u003eThe matryoshka doll method 166\u003c\/p\u003e \u003cp\u003eArc Length 168\u003c\/p\u003e \u003cp\u003eImproper Integrals 171\u003c\/p\u003e \u003cp\u003eImproper integrals with vertical asymptotes 171\u003c\/p\u003e \u003cp\u003eImproper integrals with infinite limits of integration 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12: Eight Things to Remember \u003c\/b\u003e\u003cb\u003e175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003ea\u003csup\u003e2\u003c\/sup\u003e- b\u003csup\u003e2\u003c\/sup\u003e = \u003c\/i\u003e(\u003ci\u003ea - b\u003c\/i\u003e)(\u003ci\u003ea + b\u003c\/i\u003e) 175\u003c\/p\u003e \u003cp\u003e\u003ci\u003e0\/5 = 0 \u003c\/i\u003eBut \u003ci\u003e5\/0 \u003c\/i\u003eis Undefined 175\u003c\/p\u003e \u003cp\u003eSohCahToa 175\u003c\/p\u003e \u003cp\u003eTrig Values to Know 176\u003c\/p\u003e \u003cp\u003e\u003ci\u003esin\u003csup\u003e2\u003c\/sup\u003e\u003c\/i\u003e\u003ci\u003eϴ + cos\u003csup\u003e2\u003c\/sup\u003eϴ = 1 \u003c\/i\u003e176\u003c\/p\u003e \u003cp\u003eThe Product Rule 176\u003c\/p\u003e \u003cp\u003eThe Quotient Rule 176\u003c\/p\u003e \u003cp\u003eYour Sunglasses 176\u003c\/p\u003e \u003cp\u003eIndex 177\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407093932375,"sku":"9781119591207","price":10.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119591207.jpg?v=1730498154"},{"product_id":"calculus-early-transcendentals-single-variable-9781319018870","title":"Calculus Early Transcendentals Single Variable","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Macmillan Learning","offers":[{"title":"Default Title","offer_id":49407407849815,"sku":"9781319018870","price":69.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781319018870.jpg?v=1730499284"},{"product_id":"calculus-in-context-9781421422305","title":"Calculus in Context","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus in Context is a compelling exploration-for students and instructors alike-of a discipline that is both rich in conceptual beauty and broad in its applied relevance.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe depth of detail in each application [offered by \u003ci\u003eCalculus in Context\u003c\/i\u003e] provides an excellent structure for guiding students through the “why should we care” moments that every calculus class experiences.\u003cbr\u003e—\u003ci\u003eMathematical Association of America\u003c\/i\u003e\u003cbr\u003eRecommended.\u003cbr\u003e—\u003ci\u003eChoice\u003c\/i\u003e\u003cbr\u003eHahn's book is the perfect choice for college and university teachers who want to teach calculus with reference to its origins and applications.\u003cbr\u003e—\u003ci\u003eZentralblatt Math\u003c\/i\u003e\u003cbr\u003eVery well written in an engaging and enthusiastic style: it is very suitable for first year students, is perhaps not too demanding for students about to enter university, and it is particularly useful to those with more than a passing interest in astronomy. There is plenty to learn for the reader, and the massive text is also a good reference book on calculus. This labour of love from the author more than satisfies the high hopes for a good calculus book... and I highly recommend it.\u003cbr\u003e—Peter Shiu, \u003ci\u003eMathematical Gazette\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface\u003cbr\u003e\u003cb\u003ePart I\u003c\/b\u003e\u003cbr\u003e1. The Astronomy and Geometry of the Greeks\u003cbr\u003e1.1. The Greeks Explain the Universe\u003cbr\u003e1.2. Achieving the Impossible?\u003cbr\u003e1.3. Greek Geometry\u003cbr\u003e1.4. The Pythagorean Theorem\u003cbr\u003e1.5. The Radian Measure of an Angle\u003cbr\u003e1.6. Greek Trigonometry\u003cbr\u003e1.7. Aristarchus Sizes Up the Universe\u003cbr\u003e1.8. Problems and Projects\u003cbr\u003e2. The Genius of Archimedes\u003cbr\u003e2.1. The Conic Sections\u003cbr\u003e2.2. The Question of Area\u003cbr\u003e2.3. Playing with Squares\u003cbr\u003e2.4. The Area of a Parabolic Section\u003cbr\u003e2.5. The Method of Archimedes\u003cbr\u003e2.6. Problems and Projects\u003cbr\u003e3. A New Astronomy\u003cbr\u003e3.1. A Fixed Sun at the Center\u003cbr\u003e3.2. Copernicus's Model of Earth's Orbit\u003cbr\u003e3.3. About the Distances of the Planets from the Sun\u003cbr\u003e3.4. Tycho Brahe and Parallax\u003cbr\u003e3.5. Kepler's Elliptical Orbits\u003cbr\u003e3.6. The Studies of Galileo\u003cbr\u003e3.7. The Size of the Solar System\u003cbr\u003e3.8. Problems and Projects\u003cbr\u003e4. The Coordinate Geometry of Descartes\u003cbr\u003e4.1. The Real Numbers\u003cbr\u003e4.2. The Coordinate Plane\u003cbr\u003e4.3. About the Parabola\u003cbr\u003e4.4. About the Ellipse\u003cbr\u003e4.5. Quadratic Equations in x and y\u003cbr\u003e4.6. Circles and Trigonometry\u003cbr\u003e4.7. Problems and Projects\u003cbr\u003e5. The Calculus of Leibniz\u003cbr\u003e5.1. Straight Lines\u003cbr\u003e5.2. Tangent Lines to Curves\u003cbr\u003e5.3. The Function Concept\u003cbr\u003e5.4. The Derivative of a Function\u003cbr\u003e5.5. Fermat, Kepler, and Wine Barrels\u003cbr\u003e5.6. The Definite Integral\u003cbr\u003e5.7. Cavalieri's Principle\u003cbr\u003e5.8. Differentials and the Fundamental Theorem\u003cbr\u003e5.9. Volumes of Revolution\u003cbr\u003e5.10. Problems and Projects\u003cbr\u003e6. The Calculus of Newton\u003cbr\u003e6.1. Simple Functions and Areas\u003cbr\u003e6.2. The Derivative of a Simple Function\u003cbr\u003e6.3. From Simple Functions to Power Series\u003cbr\u003e6.4. The Mathematics of a Moving Point\u003cbr\u003e6.5. Galileo and Acceleration\u003cbr\u003e6.6. Dealing with Forces\u003cbr\u003e6.7. The Trajectory of a Projectile\u003cbr\u003e6.8. Newton Studies the Motion of the Planets\u003cbr\u003e6.9. Connecting Force and Geometry\u003cbr\u003e6.10. The Law of Universal Gravitation\u003cbr\u003e6.11. Problems and Projects\u003cbr\u003e\u003cb\u003ePart II\u003c\/b\u003e\u003cbr\u003e7. Differential Calculus\u003cbr\u003e7.1. Mathematical Functions\u003cbr\u003e7.2. A Study of Limits\u003cbr\u003e7.3. Continuous Functions\u003cbr\u003e7.4. Differentiable Functions\u003cbr\u003e7.5. Computing Derivatives\u003cbr\u003e7.6. Some Theoretical Concerns\u003cbr\u003e7.7. Derivatives of Trigonometric Functions\u003cbr\u003e7.8. Understanding Functions\u003cbr\u003e7.9. Graphing Functions\u003cbr\u003e7.10. Exponential Functions\u003cbr\u003e7.11. Logarithm Functions\u003cbr\u003e7.12. Hyperbolic Functions\u003cbr\u003e7.13. Final Comments about Graphs\u003cbr\u003e7.14. Problems and Projects\u003cbr\u003e8. Applications of Differential Calculus\u003cbr\u003e8.1. Derivatives as Rates of Change\u003cbr\u003e8.1.1. Growth of Organisms\u003cbr\u003e8.1.2. Radioactive Decay\u003cbr\u003e8.1.3. Cost of Production\u003cbr\u003e8.2. The Pulley Problem of L'Hospital\u003cbr\u003e8.2.1. The Solution Using Calculus\u003cbr\u003e8.2.2. The Solution by Balancing Forces\u003cbr\u003e8.3. The Suspension Bridge\u003cbr\u003e8.4. An Experiment of Galileo\u003cbr\u003e8.4.1. Sliding Ice Cubes and Spinning Wheels\u003cbr\u003e8.4.2. Torque and Rotational Inertia\u003cbr\u003e8.4.3. The Mathematics behind Galileo's Experiment\u003cbr\u003e8.5. From Fermat's Principle to the Reflecting Telescope\u003cbr\u003e8.5.1. Fermat's Principle and the Reflection of Light\u003cbr\u003e8.5.2. The Refraction of Light\u003cbr\u003e8.5.3. About Lenses\u003cbr\u003e8.5.4. Refracting and Reflecting Telescopes\u003cbr\u003e8.6. Problems and Projects\u003cbr\u003e9. The Basics of Integral Calculus\u003cbr\u003e9.1. The Definite Integral of a Function\u003cbr\u003e9.2. Volume and the Definite Integral\u003cbr\u003e9.3. Lengths of Curves and the Definite Integral\u003cbr\u003e9.4. Surface Area and the Definite Integral\u003cbr\u003e9.5. The Definite Integral and the Fundamental Theorem\u003cbr\u003e9.6. Area as Antiderivative\u003cbr\u003e9.7. Finding Antiderivatives\u003cbr\u003e9.7.1. Integration by Substitution\u003cbr\u003e9.7.2. Integration by Parts\u003cbr\u003e9.7.3. Some Algebraic Moves\u003cbr\u003e9.8. Inverse Functions\u003cbr\u003e9.9. Inverse Trigonometric and Hyperbolic Functions\u003cbr\u003e9.9.1. Trigonometric Inverses\u003cbr\u003e9.9.2. Hyperbolic Inverses\u003cbr\u003e9.10. Trigonometric and Hyperbolic Substitutions\u003cbr\u003e9.11. Some Integral Formulas\u003cbr\u003e9.12. The Trapezoidal and Simpson Rules\u003cbr\u003e9.13. One Loop of the Sine Curve\u003cbr\u003e9.14. Problems and Projects\u003cbr\u003e10. Applications of Integral Calculus\u003cbr\u003e10.1. Estimating the Weight of Domes\u003cbr\u003e10.1.1. The Hagia Sophia\u003cbr\u003e10.1.2. The Roman Pantheon\u003cbr\u003e10.2. The Cables of a Suspension Bridge\u003cbr\u003e10.3. From Pocket Watch to Pseudosphere\u003cbr\u003e10.3.1. Volume and Surface Area of Revolution of the Tractrix\u003cbr\u003e10.3.2. The Pseudosphere\u003cbr\u003e10.4. Calculating the Motion of a Planet\u003cbr\u003e10.4.1. Determining Position in Terms of Time\u003cbr\u003e10.4.2. Determining Speed and Direction\u003cbr\u003e10.4.3. Earth, Jupiter, and Halley\u003cbr\u003e10.5. Integral Calculus and the Action of Forces\u003cbr\u003e10.5.1. Work and Energy, Impulse and Momentum\u003cbr\u003e10.5.2. Analysis of Springs\u003cbr\u003e10.5.3. The Force in a Gun Barrel\u003cbr\u003e10.5.4. The Springfield Rifle\u003cbr\u003e10.6. Problems and Projects\u003cbr\u003e11. Basics of Differential Equations\u003cbr\u003e11.1. First-Order Separable Differential Equations\u003cbr\u003e11.2. The Method of Integrating Factors\u003cbr\u003e11.3. Direction Fields and Euler's Method\u003cbr\u003e11.4. The Polar Coordinate System\u003cbr\u003e11.5. The Complex Plane\u003cbr\u003e11.6. Second-Order Differential Equations\u003cbr\u003e11.7. The Basics of Power Series\u003cbr\u003e11.8. Taylor and Maclaurin Series\u003cbr\u003e11.9. Solving a Second-Order Differential Equation\u003cbr\u003e11.10. Free Fall with Air Resistance\u003cbr\u003e11.10.1. Going Up\u003cbr\u003e11.10.2. Coming Down\u003cbr\u003e11.10.3. Bullets and Ping-Pong Balls\u003cbr\u003e11.11. Systems with Springs and Damping Elements\u003cbr\u003e11.11.1. The Family Sedan and the Stock Car\u003cbr\u003e11.12. More about Hanging Cables\u003cbr\u003e11.13. Problems and Projects\u003cbr\u003e12. Polar Calculus and Newton's Planetary Orbits\u003cbr\u003e12.1. Graphing Polar Equations\u003cbr\u003e12.2. The Conic Sections in Polar Coordinates\u003cbr\u003e12.3. The Derivative of a Polar Function\u003cbr\u003e12.4. The Lengths of Polar Curves\u003cbr\u003e12.5. Areas in Polar Coordinates\u003cbr\u003e12.6. Equiangular Spirals\u003cbr\u003e12.7. Centripetal Force in Cartesian Coordinates\u003cbr\u003e12.8. Going Polar\u003cbr\u003e12.9. From Conic Section to Inverse Square Law and Back Again\u003cbr\u003e12.10. Gravity and Geometry\u003cbr\u003e12.11. Spiral Galaxies\u003cbr\u003e12.12. Problems and Projects\u003cbr\u003eReferences\u003cbr\u003eImage Credits and Notes\u003cbr\u003eIndex\u003c\/p\u003e","brand":"Johns Hopkins University Press","offers":[{"title":"Default Title","offer_id":49408121766231,"sku":"9781421422305","price":80.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781421422305.jpg?v=1730501664"}],"url":"https:\/\/bookcurl.com\/collections\/calculus.oembed?page=14","provider":"Book Curl","version":"1.0","type":"link"}