{"title":"Calculus and mathematical analysis Books","description":"","products":[{"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":"mathematical-analysis-a-very-short-introduction-very-short-introductions-9780198868910","title":"Mathematical Analysis A Very Short Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eVery Short Introductions: Brilliant, sharp, inspiringThe 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn''t until the 18th and 19th centuries that mathematicians--especially Bolzano, Cauchy, and Weierstrass--began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis.This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgements 1: Taming Infinity 2: All change... 3: Should I believe my computer? 4: Dimensions aplenty 5: I'll name that tune in... 6: Putting the i in analysis 7: But there's more... Appendix Historical timeline References Further Reading Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732823126359,"sku":"9780198868910","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198868910.jpg?v=1719998550"},{"product_id":"functions-of-one-complex-variable-i-9780387903286","title":"Functions of One Complex Variable I","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study.\"   --MathSciNet\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI. The Complex Number System.- §1. The real numbers.- §2. The field of complex numbers.- §3. The complex plane.- §4. Polar representation and roots of complex numbers.- §5. Lines and half planes in the complex plane.- §6. The extended plane and its spherical representation.- II. Metric Spaces and the Topology of ?.- §1. Definition and examples of metric spaces.- §2. Connectedness.- §3. Sequences and completeness.- §4. Compactness.- §5. Continuity.- §6. Uniform convergence.- III. Elementary Properties and Examples of Analytic Functions.- §1. Power series.- §2. Analytic functions.- §3. Analytic functions as mapping, Möbius transformations.- IV. Complex Integration.- §1. Riemann-Stieltjes integrals.- §2. Power series representation of analytic functions.- §3. Zeros of an analytic function.- §4. The index of a closed curve.- §5. Cauchy’s Theorem and Integral Formula.- §6. The homotopic version of Cauchy’s Theorem and simple connectivity.- §7. Counting zeros; the Open Mapping Theorem.- §8. Goursat’s Theorem.- V. Singularities.- §1. Classification of singularities.- §2. Residues.- §3. The Argument Principle.- VI. The Maximum Modulus Theorem.- §1. The Maximum Principle.- §2. Schwarz’s Lemma.- §3. Convex functions and Hadamard’s Three Circles Theorem.- §4. Phragm\u0026gt;én-Lindel\u0026gt;üf Theorem.- VII. Compactness and Convergence in ihe Space of Analytic Functions.- §1. The space of continuous functions C(G, ?).- §2. Spaccs of analytic functions.- §3. Spaccs of meromorphic functions.- §4. The Riemann Mapping Theorem.- §5. Weierstrass Factorization Theorem.- §6. Factorization of the sine function.- $7. The gamma function.- §8. The Riemann zeta function.- VIII. Runge’s Theorem.- §1. Runge’s Theorem.- §2. Simple connectedness.- §3. Mittag-Leffler’s Theorem.- IX. Analytic Continuation and Riemann Surfaces.- §1. Schwarz Reflection Principle.- $2. Analytic Continuation Along A Path.- §3. Monodromy Theorem.- §4. Topological Spaces and Neighborhood Systems.- $5. The Sheaf of Germs of Analytic Functions on an Open Set.- $6. Analytic Manifolds.- §7. Covering spaccs.- X. Harmonic Functions.- §1. Basic Properties of harmonic functions.- §2. Harmonic functions on a disk.- §3. Subharmonic and superharmonic functions.- §4. The Dirichlet Problem.- §5. Green’s Functions.- XI. Entire Functions.- §1. Jensen’s Formula.- §2. The genus and order of an entire function.- §3. Hadamard Factorization Theorem.- XII. The Range of an Analytic Function.- §1. Bloch’s Theorem.- §2. The Little Picard Theorem.- §3. Schottky’s Theorem.- §4. The Great Picard Theorem.- Appendix A: Calculus for Complex Valued Functions on an Interval.- Appendix B: Suggestions for Further Study and Bibliographical Notes.- References.- List of Symbols.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726507351,"sku":"9780387903286","price":40.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387903286.jpg?v=1720001405"},{"product_id":"complex-analysis-9780387950693","title":"Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFirst Part.- I The Complex Plane and Elementary Functions.- II Analytic Functions.- III Line Integrals and Harmonic Functions.- IV Complex Integration and Analyticity.- V Power Series.- VI Laurent Series and Isolated Singularities.- VII The Residue Calculus.- Second Part.- VIII The Logarithmic Integral.- IX The Schwarz Lemma and Hyperbolic Geometry.- X Harmonic Functions and the Reflection Principle.- XI Conformal Mapping.- Third Part.- XII Compact Families of Meromorphic Functions.- XIII Approximation Theorems.- XIV Some Special Functions.- XV The Dirichlet Problem.- XVI Riemann Surfaces.- Hints and Solutions for Selected Exercises.- References.- List of Symbols.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* The Complex Plane and Elementary Functions * Analytic Functions * Line Integrals and Harmonic Functions * Complex Integration and Analyticity * Power Series * Laurent Series and Isolated Singularities * The Residue Calculus * The Logarithmic Integral * The Schwarz Lemma and Hyperbolic Geometry * Harmonic Functions and the Reflection Principle * Conformal Mapping * Compact Families of Meromorphic Functions * Approximation Theorems * Some Special Functions * The Dirichlet Problem * Riemann Surfaces","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726998871,"sku":"9780387950693","price":41.24,"currency_code":"GBP","in_stock":true}]},{"product_id":"padic-numbers-padic-analysis-and-zetafunctions-9780387960173","title":"padic Numbers padic Analysis and ZetaFunctions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“In the second edition of this text, Koblitz presents a wide-ranging introduction to the theory of p-adic numbers and functions. … there are some really nice exercises that allow the reader to explore the material. … And with the exercises, the book would make a good textbook for a graduate course, provided the students have a decent background in analysis and number theory.” (Donald L. Vestal, The Mathematical Association of America, April, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI p-adic numbers.- 1. Basic concepts.- 2. Metrics on the rational numbers.- Exercises.- 3. Review of building up the complex numbers.- 4. The field of p-adic numbers.- 5. Arithmetic in ?p.- Exercises.- II p-adic interpolation of the Riemann zeta-function.- 1. A formula for ?(2k).- 2. p-adic interpolation of the function f(s) = as.- Exercises.- 3. p-adic distributions.- Exercises.- 4. Bernoulli distributions.- 5. Measures and integration.- Exercises.- 6. The p-adic ?-function as a Mellin-Mazur transform.- 7. A brief survey (no proofs).- Exercises.- III Building up ?.- 1. Finite fields.- Exercises.- 2. Extension of norms.- Exercises.- 3. The algebraic closure of ?p.- 4. ?.- Exercises.- IV p-adic power series.- 1. Elementary functions.- Exercises.- 2. The logarithm, gamma and Artin-Hasse exponential functions.- Exercises.- 3. Newton polygons for polynomials.- 4. Newton polygons for power series.- Exercises.- V Rationality of the zeta-function of a set of equations over a finite field.- 1. Hypersurfaces and their zeta-functions.- Exercises.- 2. Characters and their lifting.- 3. A linear map on the vector space of power series.- 4. p-adic analytic expression for the zeta-function.- Exercises.- 5. The end of the proof.- Answers and Hints for the Exercises.  ","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727097175,"sku":"9780387960173","price":64.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"differential-equations-and-their-applications-9780387978949","title":"Differential Equations and Their Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eChapter 1 First-order differential equations * Chapter 2 Second-order linear differential equations * Chapter 3 Systems of differential equations * Chapter 4 Qualitative theory of differential equations * Chapter 5 Separation of variables and Fourier series * Chapter 6 Sturm -Liouville boundary value problems * Appendix A Some simple facts concerning functions of several variables * Appendix B Sequences and series * Appendix C C Programs * Answers to odd-numbered exercises * Index\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1 First-order differential equations * Chapter 2 Second-order linear differential equations * Chapter 3 Systems of differential equations * Chapter 4 Qualitative theory of differential equations * Chapter 5 Separation of variables and Fourier series * Chapter 6 Sturm -Liouville boundary value problems * Appendix A Some simple facts concerning functions of several variables * Appendix B Sequences and series * Appendix C C Programs * Answers to odd-numbered exercises * Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727949143,"sku":"9780387978949","price":46.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387978949.jpg?v=1720001409"},{"product_id":"complex-analysis-9780387985923","title":"Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne Basic Theory.- I Complex Numbers and Functions.- II Power Series.- III Cauchy's Theorem, First Part.- IV Winding Numbers and Cauchy's Theorem.- V Applications of Cauchy's integral Formula.- VI Calculus of Residues.- VII Conformal Mappings.- VIII Harmonic Functions.- Two Geometric Function Theory.- IX Schwarz Reflection.- X The Riemann Mapping Theorem.- XI Analytic Continuation Along Curves.- Three Various Analytic Topics.- XII Applications of the Maximum Modulus Principle and Jensen's Formula.- XIII Entire and Meromorphic Functions.- XIV Elliptic Functions.- XV The Gamma and Zeta Functions.- XVI The Prime Number Theorem.- 1. Summation by Parts and Non-Absolute Convergence.- 2. Difference Equations.- 3. Analytic Differential Equations.- 4. Fixed Points of a Fractional Linear Transformation.- 6. Cauchy's Theorem for Locally Integrable Vector Fields.- 7. More on Cauchy-Riemann.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"\u003cem\u003eThe very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers.\"\u003cbr\u003e\u003c\/em\u003eEMS Newsletter, Vol. 37, Sept. 2000\u003c\/p\u003e \u003cp\u003eFourth Edition\u003c\/p\u003e \u003cp\u003e\u003cem\u003eS. Lang\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003eComplex Analysis\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"A highly recommendable book for a two semester course on complex analysis.\"\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e—ZENTRALBLATTMATH\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI: BASIC THEORY. 1: Complex Numbers and Functions. 2: Power Series. 3: Cauchy's Theorem, First Part. 4: Winding Numbers and Cauchy's Theorem. 5: Applications of Cauchy's Integral Formula. 6: Calculus of Residues. 7: Conformal Mappings. 8: Harmonic Functions. II: GEOMETRIC FUNCTION THEORY. 9: Schwarz Reflection. 10: The Riemann Mapping Theorem. 11: Analytic Continuation Along Curves. III: VARIOUS ANALYTIC TOPICS. 12: Applications of the Maximum Modulus Principle and Jensen's Formula. 13: Entire and Meromorphic Functions. 14: Elliptic Functions. 15: The Gamma and Zeta Functions. 16: The Prime Number Theorem.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733728309591,"sku":"9780387985923","price":53.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387985923.jpg?v=1720001411"},{"product_id":"advanced-mathematical-methods-for-scientists-and-engineers-i-9780387989310","title":"Advanced Mathematical Methods for Scientists and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This book is a reprint of the original published by McGraw-Hill \\ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, \"Asymptotic methods and perturbation theory\". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. \u003cbr\u003e\u003cbr\u003eThis is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic.\"  (A.D. Wood, Mathematical Reviews) \u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733728375127,"sku":"9780387989310","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387989310.jpg?v=1720001411"},{"product_id":"calculus-9781009159692","title":"Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski''s version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; 1. Real Numbers and Functions; 2. Integration; 3. Limits and Continuity; 4. Differentiation; 5. Techniques of Integration; 6. Mean Value Theorems and Applications; 7. Sequences and Series; 8. Taylor and Fourier Series; A. Solutions to Odd-Numbered Exercises; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738007220567,"sku":"9781009159692","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009159692.jpg?v=1723811676"},{"product_id":"functional-analysis-9781009243902","title":"Functional Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook is designed for a year-long introductory course in Functional Analysis and the theory of Operator Algebras. It guides graduate students and researchers through a wide range of topics including Hilbert spaces, Weak Topologies and C*-algebras. With numerous problems and examples, it is suitable for classroom teaching and self-learning.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Notation; 1. Preliminaries; 2. Normed Linear Spaces; 3. Hilbert Spaces; 4. Dual Spaces; 5. Operators on Banach Spaces; 6. Weak Topologies; 7. Spectral Theory; 8. C*-Algebras; 9. Measure and Integration; 10. Normal Operators on Hilbert Spaces; Appendices; A.1 The Stone–Weierstrass Theorem; A.2 The Radon–Nikodym Theorem; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738022031703,"sku":"9781009243902","price":37.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009243902.jpg?v=1723811685"},{"product_id":"college-algebra-9781292042343","title":"College Algebra","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\u003eP. Prerequisites: Fundamental Concepts of Algebra\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eP.1 Algebraic Expressions, Mathematical Models, and Real Numbers\u003c\/p\u003e \u003cp\u003eP.2 Exponents and Scientific Notation\u003c\/p\u003e \u003cp\u003eP.3 Radicals and Rational Exponents\u003c\/p\u003e \u003cp\u003eP.4 Polynomials\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003eP.5 Factoring Polynomials\u003c\/p\u003e \u003cp\u003eP.6 Rational Expressions\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER P TEST\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Equations and Inequalities\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Graphs and Graphing Utilities\u003c\/p\u003e \u003cp\u003e1.2 Linear Equations and Rational Equations\u003c\/p\u003e \u003cp\u003e1.3 Models and Applications\u003c\/p\u003e \u003cp\u003e1.4 Complex Numbers\u003c\/p\u003e \u003cp\u003e1.5 Quadratic Equations\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e1.6 Other Types of Equations\u003c\/p\u003e \u003cp\u003e1.7 Linear Inequalities and Absolute Value Inequalities\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 1 TEST\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Functions and Graphs\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basics of Functions and Their Graphs\u003c\/p\u003e \u003cp\u003e2.2 More on Functions and Their Graphs\u003c\/p\u003e \u003cp\u003e2.3 Linear Functions and Slope\u003c\/p\u003e \u003cp\u003e2.4 More on Slope\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e2.5 Transformations of Functions\u003c\/p\u003e \u003cp\u003e2.6 Combinations of Functions; Composite Functions\u003c\/p\u003e \u003cp\u003e2.7 Inverse Functions\u003c\/p\u003e \u003cp\u003e2.8 Distance and Midpoint Formulas; Circles\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 2 TEST\u003c\/p\u003e \u003cp\u003e   CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Polynomial and Rational Functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Quadratic Functions\u003c\/p\u003e \u003cp\u003e3.2 Polynomial Functions and Their Graphs\u003c\/p\u003e \u003cp\u003e3.3 Dividing Polynomials; Remainder and Factor Theorems\u003c\/p\u003e \u003cp\u003e3.4 Zeros of Polynomial Functions\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e3.5 Rational Functions and Their Graphs\u003c\/p\u003e \u003cp\u003e3.6 Polynomial and Rational Inequalities\u003c\/p\u003e \u003cp\u003e3.7 Modeling Using Variation\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 3 TEST\u003c\/p\u003e \u003cp\u003e   CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Exponential and Logarithmic Functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Exponential Functions\u003c\/p\u003e \u003cp\u003e4.2 Logarithmic Functions\u003c\/p\u003e \u003cp\u003e4.3 Properties of Logarithms\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e4.4 Exponential and Logarithmic Equations\u003c\/p\u003e \u003cp\u003e4.5 Exponential Growth and Decay; Modeling Data\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 4 TEST\u003c\/p\u003e \u003cp\u003e   CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Systems of Equations and Inequalities\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Systems of Linear Equations in Two Variables\u003c\/p\u003e \u003cp\u003e5.2 Systems of Linear Equations in Three Variables\u003c\/p\u003e \u003cp\u003e5.3 Partial Fractions\u003c\/p\u003e \u003cp\u003e5.4 Systems of Nonlinear Equations in Two Variables\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e5.5 Systems of Inequalities\u003c\/p\u003e \u003cp\u003e5.6 Linear Programming\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 5 TEST\u003c\/p\u003e \u003cp\u003e   CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Matrices and Determinants\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Matrix Solutions to Linear Systems\u003c\/p\u003e \u003cp\u003e6.2 Inconsistent and Dependent Systems and Their Applications\u003c\/p\u003e \u003cp\u003e6.3 Matrix Operations and Their Applications\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e6.4 Multiplicative Inverses of Matrices and Matrix Equations\u003c\/p\u003e \u003cp\u003e6.5 Determinants and Cramer's Rule\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 6 TEST\u003c\/p\u003e \u003cp\u003e   CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Conic Sections\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Ellipse\u003c\/p\u003e \u003cp\u003e7.2 The Hyperbola\u003c\/p\u003e \u003cp\u003e   Mid-Chapter Check Point\u003c\/p\u003e \u003cp\u003e7.3 The Parabola\u003c\/p\u003e \u003cp\u003e   SUMMARY, REVIEW, AND TEST\u003c\/p\u003e \u003cp\u003e   REVIEW EXERCISES\u003c\/p\u003e \u003cp\u003e   CHAPTER 7 TEST\u003c\/p\u003e","brand":"Pearson Education Limited","offers":[{"title":"Default Title","offer_id":48738518991191,"sku":"9781292042343","price":64.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292042343.jpg?v=1723812112"},{"product_id":"mathematical-aspects-of-deep-learning-9781316516782","title":"Mathematical Aspects of Deep Learning","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. The modern mathematics of deep learning Julius Berner, Philipp Grohs, Gitta Kutyniok and Philipp Petersen; 2. Generalization in deep learning Kenji Kawaguchi, Leslie Pack Kaelbling, and Yoshua Bengio; 3. Expressivity of deep neural networks Ingo Gühring, Mones Raslan and Gitta Kutyniok; 4. Optimization landscape of neural networks René Vidal, Zhihui Zhu and Benjamin D. Haeffele; 5. Explaining the decisions of convolutional and recurrent neural networks Wojciech Samek, Leila Arras, Ahmed Osman, Grégoire Montavon and Klaus-Robert Müller; 6. Stochastic feedforward neural networks: universal approximation Thomas Merkh and Guido Montúfar; 7. Deep learning as sparsity enforcing algorithms A. Aberdam and J. Sulam; 8. The scattering transform Joan Bruna; 9. Deep generative models and inverse problems Alexandros G. Dimakis; 10. A dynamical systems and optimal control approach to deep learning Weinan E, Jiequn Han and Qianxiao Li; 11. Bridging many-body quantum physics and deep learning via tensor networks Yoav Levine, Or Sharir, Nadav Cohen and Amnon Shashua.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738561392983,"sku":"9781316516782","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781316516782.jpg?v=1720049471"},{"product_id":"advanced-mathematical-methods-for-scientists-and-engineers-i-9781441931870","title":"Advanced Mathematical Methods for Scientists and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This book is a reprint of the original published by McGraw-Hill \\ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, \"Asymptotic methods and perturbation theory\". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. \u003cbr\u003e\u003cbr\u003eThis is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic.\"  (A.D. Wood, Mathematical Reviews) \u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739209675095,"sku":"9781441931870","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"advanced-calculus-9781441973313","title":"Advanced Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWith a fresh geometric approach that incorporates more than 250  illustrations, this textbook sets itself apart from all others in  advanced calculus.  Besides the classical  capstones--the change of variables formula, implicit and inverse  function theorems, the integral theorems of Gauss and Stokes--the text  treats other important topics in differential analysis, such as Morse''s  lemma and the Poincaré lemma.  The ideas behind  most topics can be understood with just two or three variables.  The book  incorporates modern computational tools to give visualization real  power.  Using 2D and 3D graphics, the book offers new  insights into fundamental elements of the calculus of differentiable  maps.  The geometric theme  continues with an analysis of the physical meaning of the divergence and  the curl at a level of detail not found in other advanced calculus  books.  This is a  textbook for undergraduates and graduate students in mathematics, the  physical sciences, and economics.  Prerequisites  are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on  advanced calculus and for a variety of semester courses--including  topics in geometry.  The measured pace of  the book, with its extensive examples and illustrations, make it  especially suitable for independent study.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)\u003c\/p\u003e\u003cp\u003e“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)\u003c\/p\u003e\u003cp\u003e“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739210068311,"sku":"9781441973313","price":53.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441973313.jpg?v=1720051499"},{"product_id":"complex-analysis-9781441972874","title":"Complex Analysis","description":"\u003cp\u003eThis unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.\u003c\/p\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739210166615,"sku":"9781441972873","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441972873.jpg?v=1720051499"},{"product_id":"an-introduction-to-infinite-products-9783030906450","title":"An Introduction to Infinite Products","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues.  The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates.  The exercises give the reader a good opportunity to test their understanding of each section.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This is an excellent textbook … . It must be very satisfactory for students to learn the subject from such a nicely written book.” (Marcel G. de Bruin, zbMATH 1491.40001, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Introduction.- 2. Infinite Products.- 3. The Gamma Function.- 4. Prime Numbers, Partitions and Products.- 5. Epilogue.- 6. Tables of Products.- References.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743057391959,"sku":"9783030906450","price":29.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"difference-matrices-for-ode-and-pde-a-matlab-r-companion-9783031119996","title":"Difference Matrices for ODE and PDE: A MATLAB®","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is pedagogically novel. This unique and concise textbook gives the reader easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB which approximate ordinary and partial differential equations. Prerequisites include a knowledge of basic calculus, linear algebra, and ordinary differential equations. Some knowledge of partial differential equations is a plus though the text may easily serve as a supplement for the student currently working through an introductory PDEs course.  Familiarity with MATLAB is not required though a little prior experience with programming would be helpful.\u003c\/p\u003e  In addition to its special focus on solving in MATLAB, the abundance of examples and exercises make this text versatile in use. It would serve well in a graduate course in introductory scientific computing for partial differential equations. With prerequisites mentioned above plus some elementary numerical analysis, most of the material can be covered and many of the exercises assigned in a single semester course. Some of the more challenging exercises make substantial projects and relate to topics from other typical graduate mathematics courses, e.g., linear algebra, differential equations, or topics in nonlinear functional analysis. A selection of the exercises may be assigned as projects throughout the semester. The student will develop the skills to run simulations corresponding to the primarily theoretical course material covered by the instructor. The book can serve as a supplement for the instructor teaching any course in differential equations. Many of the examples can be easily implemented and the resulting simulation demonstrated by the instructor. If the course has a numerical component, a few of the more difficult exercises may be assigned as student projects.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e  Established researchers in theoretical partial differential equations may find this book useful as well, particularly as an introductory guide for their research students. Those unfamiliar with MATLAB can use the material as a reference to quickly develop their own applications in that language. Practical assistance in implementing algorithms in MATLAB can be found in these pages. A mathematician who is new to the practical implementation of methods for scientific computation in general can learn how to implement and execute numerical simulations of differential equations in MATLAB with relative ease by working through a selection of exercises. Additionally, the book can serve as a practical guide in independent study, undergraduate or graduate research experiences, or for reference in simulating solutions to specific thesis or dissertation-related experiments.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Review of elementary numerical methods and MATLAB(R).- 3. Ordinary Differential Equations.- 4. Partial Differential Equations.- 5. Advanced topics in semilinear elliptic BVP.- References.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743070859607,"sku":"9783031119996","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"a-circle-line-study-of-mathematical-analysis-9783031197376","title":"A Circle-Line Study of Mathematical Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann.\u003cbr\u003e \u003cbr\u003e The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003eThe book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePart I First half of the journey.- 1 An appetizer of propositional logic.- 2 Sets, relations, functions in a naïve way.- 3 Numbers.- 4 Elementary cardinality.- 5 Distance, topology and sequences on the set of real numbers.- 6 Series.- 7 Limits: from sequences to functions of a real variable.- 8 Continuous functions of a real variable.- 9 Derivatives and differentiability- 10 Riemann’s integral.- 11 Elementary functions.- Part II Second half of the journey.- 12 Return to Set Theory.- 13 Neighbors again: topological spaces.- 14 Differentiating again: linearization in normed spaces.- 15 A functional approach to Lebesgue integration theory.- 16 Measures before integrals.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743075053911,"sku":"9783031197376","price":42.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031197376.jpg?v=1720063999"},{"product_id":"more-almost-impossible-integrals-sums-and-series-a-new-collection-of-fiendish-problems-and-surprising-solutions-9783031212611","title":"More (Almost) Impossible Integrals, Sums, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book, the much-anticipated sequel to \u003ci\u003e(Almost) Impossible, Integrals, Sums, and Series\u003c\/i\u003e, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author’s previous book, these fascinating mathematical problems are shown in new and engaging ways, and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren’t afraid of a challenge.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1. Integrals.- Chapter 2. Hints.- Chapter 3. Solutions.- Chapter 4. Sums and Series.- Chapter 5. Hints.- Chapter 6. Solutions.\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743076069719,"sku":"9783031212611","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"elementary-functions-9783031290749","title":"Elementary Functions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook focuses on the study of different kinds of elementary functions ubiquitous both in high school Algebra and Calculus. To analyze the functions ranging from polynomial to trigonometric ones, it uses rudimentary techniques available to high school students, and at the same time follows the mathematical rigor appropriate for university level courses.\u003cbr\u003eContrary to other books of Pre-Calculus, this textbook emphasizes the study of elementary functions with rigor appropriate for university level courses in mathematics, although the exposition is confined to the pre-limit topics and techniques. This makes the book useful, on the one hand, as an introduction to mathematical reasoning and methods of proofs in mathematical analysis, and on the other hand, as a preparatory course on the properties of different kinds of elementary functions.\u003cbr\u003eThe textbook is aimed at university freshmen and high-school students interested in learning strict mathematical reasoning and in preparing a solid base for subsequent study of elementary functions at advanced level of Calculus and Analysis. The required prerequisites correspond to the level of the high school Algebra. All the preliminary concepts and results related to the elementary functions are covered in the initial part of the text. This makes the textbook suitable for both classroom use and self-study.  \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- 1. Sets of Numbers and Cartesian Coordinates. - 2. Functions and Their Analytic Properties. - 3. Algebraic Functions: Polynomial, Rational and Irrational. - 4. Transcendental Functions: Exponential, Logarithmic, Trigonometric. - 5. Epilogue: A Bridge to Calculus.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743079346519,"sku":"9783031290749","price":42.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031290749.jpg?v=1720064018"},{"product_id":"a-short-book-on-long-sums-infinite-series-for-calculus-students-9783031375569","title":"A Short Book on Long Sums: Infinite Series for","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are  a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. \u003c\/p\u003e  Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor’s guide with solutions to all the problems is available. \u003cp\u003e\u003c\/p\u003e  \u003cp\u003eThe book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e- To the reader.- Getting close with lines.- Getting closer with polynomials.- Going all the way: Convergence.- Power series.- Distant mountains.- Appendix A: SageMath: A (very) short introduction.- Appendix B: Why I do it this way.- Bibliography.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743084097879,"sku":"9783031375569","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031375569.jpg?v=1720064041"},{"product_id":"putnam-and-beyond-9783319589862","title":"Putnam and Beyond","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad\u003c\/p\u003eratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eUsing the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. \u003ci\u003ePutnam and Beyond\u003c\/i\u003e is organized for independent study by undergraduate and gradu\u003c\/p\u003eate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the Second Edition.- Preface to the First Edition.- A Study Guide.- 1. Methods of Proof.- 2. Algebra.- 3. Real Analysis.- 4. Geometry and Trigonometry.- 5. Number Theory.- 6. Combinatorics and Probability.- Solutions.- Index of Notation.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743099466071,"sku":"9783319589862","price":46.74,"currency_code":"GBP","in_stock":true}]},{"product_id":"multivariable-calculus-with-applications-9783319740720","title":"Multivariable Calculus with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems.\u003c\/p\u003e  Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics. \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The presentation of the material is guided by applications so that physics and engineering students will find the text engaging and see the relevance of multivariable calculus to their work. The text contains over 500 exercises with answers and\/or solutions to half provided at the back of the book, enabling students to gauge their understanding of the content as they proceed. A well-written, engaging text. Summing Up: Highly recommended. Upper-division undergraduates and professionals.” (J. T. Zerger, Choice, Vol. 56 (03), November, 2018)\u003cbr\u003e“This book belongs to a collection aimed at third- and fourth-year undergraduate mathematics students at North American universities. … There are more than 200 figures to help the reader to understand the explanations and about 500 problems. … I think this book can be recommended since, moreover, it is very pedagogical.” (Richard Becker, Mathematical Reviews, October, 2018)\u003cbr\u003e“Lax and Terrell’s sequel to their Calculus With Applications presents a first course in multivariable calculus that fits in just over 400 pages. Even instructors who use standard texts will find much of value in this refreshing first edition. The book is written with a wide range of STEM students in mind, and its exposition remains remarkably fluid without scarificing precision. Every section of each chapter ends with an excellent collection of exercises, which should be graciously welcomed by independent learners and instructors alike.” (Tushar Das, MAA Reviews, September, 2018)\u003cbr\u003e“The main achievement of the authors is that they essentially have simplified the teaching of the old topics to make a place for new ones. The proofs are exposited to encourage understanding, not meaningless rigor. … the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMATH 1396.26002, 2018)\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Vectors and matrices.- 2. Functions.- 3. Differentiation.- 4. More about differentiation.- 5. Applications to motion.- 6. Integration.- 7. Line and surface integrals.- 8.  Divergence and Stokes’ Theorems and conservation laws.- 9. Partial differential equations.-  Answers to selected problems.- Index. \u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743103758679,"sku":"9783319740720","price":50.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"a-visual-introduction-to-differential-forms-and-calculus-on-manifolds-9783319969916","title":"A Visual Introduction to Differential Forms and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e “The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book.” (Hirokazu Nishimura, zbMath 1419.58001, 2019)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e  ","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743111459159,"sku":"9783319969916","price":53.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319969916.jpg?v=1720064159"},{"product_id":"ordinary-differential-equations-9783540345633","title":"Ordinary Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFew books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. \u003c\/p\u003e \u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation.\" --SIAM REVIEW\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation … . The new edition is highly recommended as a general reference for the essential theory of ordinary differential equations and as a textbook for an introductory course for serious undergraduate or graduate students. … In the US system, it is an excellent text for an introductory graduate course.\" (Carmen Chicone, SIAM Review, Vol. 49 (2), 2007)\u003c\/p\u003e \u003cp\u003e\"Vladimir Arnold’s is a master, not just of the technical realm of differential equations but of pedagogy and exposition as well. … The writing throughout is crisp and clear. … Arnold’s says that the book is based on a year-long sequence of lectures for second-year mathematics majors in Moscow. In the U.S., this material is probably most appropriate for advanced undergraduates or first-year graduate students.\" (William J. Satzer, MathDL, August, 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasic Concepts.- Basic Theorems.- Linear Systems.- Proofs of the Main Theorems.- Differential Equations on Manifolds.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743130366295,"sku":"9783540345633","price":64.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"an-introduction-to-nonlinear-analysis-and-fixed-point-theory-9789811088650","title":"An Introduction to Nonlinear Analysis and Fixed","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in diverse applied fields. It is intended for graduate and undergraduate students of mathematics and engineering who are familiar with discrete mathematical structures, differential and integral equations, operator theory, measure theory, Banach and Hilbert spaces, locally convex topological vector spaces, and linear functional analysis.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book cover many important fundamental concepts and various techniques. It shall be very useful for both students and researchers to understand and to prepare themselves for conducting research in these two areas.” (Satit Saejung, zbMATH 1447.47002, 2020)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e​Chapter 1\u003c\/b\u003e. Fundamentals.- \u003cb\u003eChapter 2\u003c\/b\u003e. Geometry in Banach Spaces and Duality Mappings.- \u003cb\u003eChapter 3\u003c\/b\u003e. Differential Calculus in Banach Spaces.- \u003cb\u003eChapter 4\u003c\/b\u003e. Monotone Operators, Phi-accretive Operators and Their Generalizations.- \u003cb\u003eChapter 5\u003c\/b\u003e. Fixed Point Theorems.- \u003cb\u003eChapter 6\u003c\/b\u003e. Degree Theory, K-Set Contractions and Condensing Operators.- \u003cb\u003eChapter 7\u003c\/b\u003e. Random Fixed Point Theory and Monotone Operators.- \u003cb\u003eChapter 8\u003c\/b\u003e. Applications of Monotone Operator Theory to Differential and Integral Equations.- \u003cb\u003eChapter 9\u003c\/b\u003e. Applications of Fixed Point Theorems.- \u003cb\u003eChapter 10\u003c\/b\u003e. Applications of Fixed Point Theorems for Multifunction to Integral Inclusions.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743275364695,"sku":"9789811088650","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811088650.jpg?v=1720064878"},{"product_id":"basic-topology-2-topological-groups-topology-of-manifolds-and-lie-groups-9789811665769","title":"Basic Topology 2: Topological  Groups, Topology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Background on Topology, Analysis and Algebra.- 2. Topological Groups.- 3. Topology of Manifolds.- 4. Lie Groups and Lie Algebra.- 5. Brief History of Topological Groups, Manifold and Lie Groups.    ","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743290437975,"sku":"9789811665769","price":38.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811665769.jpg?v=1723812657"},{"product_id":"basic-topology-3-algebraic-topology-and-topology-of-fiber-bundles-9789811665493","title":"Basic Topology 3: Algebraic Topology and Topology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Prerequisite Concepts of Topology, Algebra and Category Theory.- 2. Homotopy Theory: Fundamental and Higher Homotopy Groups.- 3. Homology and Cohomology Theories: An Axiomatic Approach with Consequences.- 4. Topology of Fiber Bundles.- 5. Homotopy Theory of Bundles.- 6. Some Applications of Algebraic Topology.- 7. Brief History on Algebraic Topology and Fiber Bundles.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743291715927,"sku":"9789811665493","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811665493.jpg?v=1720064952"},{"product_id":"fundamentals-of-analysis-with-applications-9789811683855","title":"Fundamentals of Analysis with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743292043607,"sku":"9789811683855","price":38.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811683855.jpg?v=1720064954"},{"product_id":"what-is-calculus-from-simple-algebra-to-deep-analysis-9789814644471","title":"What Is Calculus?: From Simple Algebra To Deep","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are widely used in many disciplines. It begins with familiar elementary high school geometry and algebra, and develops important concepts such as tangents and derivatives without using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject.  This simple algebraic method is a modern version of an idea that goes back to René Descartes and that has been largely forgotten. Moving beyond algebra, the need for new analytic concepts based on completeness, continuity, and limits becomes clearly visible to the reader while investigating exponential functions.The author carefully develops the necessary foundations while minimizing the use of technical language. He expertly guides the reader to deep fundamental analysis results, including completeness, key differential equations, definite integrals, Taylor series for standard functions, and the Euler identity. This pioneering book takes the sophisticated reader from simple familiar algebra to the heart of analysis. Furthermore, it should be of interest as a source of new ideas and as supplementary reading for high school teachers, and for students and instructors of calculus and analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTangents and Double Points; Derivatives by Algebra; Exponential Functions; Completeness of Real Numbers; The Base of the Natural Exponential and Logarithm Functions; Continuity of Functions; Differentiability; Chain Rule and Other Rules for Derivatives; Derivatives of Trigonometric Functions; Mean Value Inequality and Theorem; Basic Differential Equations; Motion with Constant Acceleration; Linear and Higher Order Approximations; The Antiderivative Problem; Definite Integrals; Fundamental Theorem of Calculus; Integrability of Monotonic Functions; Integrability of Functions with Bounded Derivative; Substitution; Integration by Parts; Taylor's Theorem; Analytic Functions; The Euler Identity;","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743300071767,"sku":"9789814644471","price":58.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814644471.jpg?v=1720064992"},{"product_id":"calculus-for-business-economics-and-the-social-and-life-sciences-brief-version-9780071310710","title":"Calculus for Business Economics and the Social","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. In this book, the author applies real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1: Functions, Graphs, and Limits1.1Functions1.2The Graph of a Function1.3Lines and Linear Functions1.4Functional Models1.5Limits1.6One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1The Derivative2.2Techniques of Differentiation2.3Product and Quotient Rules; Higher-Order Derivatives2.4The Chain Rule2.5Marginal Analysis and Approximations Using Increments2.6Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Additional Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration and Differential Equations5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Distribution of Wealth and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper Integrals6.4 Introduction to Continuous ProbabilityChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation","brand":"McGraw-Hill Education - Europe","offers":[{"title":"Default Title","offer_id":48864146030935,"sku":"9780071310710","price":56.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780071310710.jpg?v=1722270599"},{"product_id":"analysis-of-ordinal-categorical-data-9780470082898","title":"Analysis of Ordinal Categorical Data","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eStatistical science   s first coordinated manual of methods for analyzing ordered categorical data, now fully revised and updated, continues to present applications and case studies in fields as diverse as sociology, public health, ecology, marketing, and pharmacy.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePreface.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003e1. Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Ordinal Categorical Scales.\u003c\/p\u003e \u003cp\u003e1.2. Advantages of Using Ordinal Methods.\u003c\/p\u003e \u003cp\u003e1.3. Ordinal Modeling Versus Ordinary Regession Analysis.\u003c\/p\u003e \u003cp\u003e1.4. Organization of This Book.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Ordinal Probabilities, Scores, and Odds Ratios.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Probabilities and Scores for an Ordered Categorical Scale.\u003c\/p\u003e \u003cp\u003e2.2. Ordinal Odds Ratios for Contingency Tables.\u003c\/p\u003e \u003cp\u003e2.3. Confidence Intervals for Ordinal Association Measures.\u003c\/p\u003e \u003cp\u003e2.4. Conditional Association in Three-Way Tables.\u003c\/p\u003e \u003cp\u003e2.5. Category Choice for Ordinal Variables.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Logistic Regression Models Using Cumulative Logits.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Types of Logits for An Ordinal Response.\u003c\/p\u003e \u003cp\u003e3.2. Cumulative Logit Models.\u003c\/p\u003e \u003cp\u003e3.3. Proportional Odds Models: Properties and Interpretations.\u003c\/p\u003e \u003cp\u003e3.4. Fitting and Inference for Cumulative Logit Models.\u003c\/p\u003e \u003cp\u003e3.5. Checking Cumulative Logit Models.\u003c\/p\u003e \u003cp\u003e3.6. Cumulative Logit Models Without Proportional Odds.\u003c\/p\u003e \u003cp\u003e3.7. Connections with Nonparametric Rank Methods.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Other Ordinal Logistic Regression Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Adjacent-Categories Logit Models.\u003c\/p\u003e \u003cp\u003e4.2. Continuation-Ratio Logit Models.\u003c\/p\u003e \u003cp\u003e4.3. Stereotype Model: Multiplicative Paired-Category Logits.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Other Ordinal Multinomial Response Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Cumulative Link Models.\u003c\/p\u003e \u003cp\u003e5.2. Cumulative Probit Models.\u003c\/p\u003e \u003cp\u003e5.3. Cumulative Log-Log Links: Proportional Hazards Modeling.\u003c\/p\u003e \u003cp\u003e5.4. Modeling Location and Dispersion Effects.\u003c\/p\u003e \u003cp\u003e5.5. Ordinal ROC Curve Estimation.\u003c\/p\u003e \u003cp\u003e5.6. Mean Response Models.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Modeling Ordinal Association Structure.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. Ordinary Loglinear Modeling.\u003c\/p\u003e \u003cp\u003e6.2. Loglinear Model of Linear-by-Linear Association.\u003c\/p\u003e \u003cp\u003e6.3. Row or Column Effects Association Models.\u003c\/p\u003e \u003cp\u003e6.4. Association Models for Multiway Tables.\u003c\/p\u003e \u003cp\u003e6.5. Multiplicative Association and Correlation Models.\u003c\/p\u003e \u003cp\u003e6.6. Modeling Global Odds Ratios and Other Associations.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Non-Model-Based Analysis of Ordinal Association.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. Concordance and Discordance Measures of Association.\u003c\/p\u003e \u003cp\u003e7.2. Correlation Measures for Contingency Tables.\u003c\/p\u003e \u003cp\u003e7.3. Non-Model-Based Inference for Ordinal Association Measures.\u003c\/p\u003e \u003cp\u003e7.4. Comparing Singly Ordered Multinomials.\u003c\/p\u003e \u003cp\u003e7.5. Order-Restricted Inference with Inequality Constraints.\u003c\/p\u003e \u003cp\u003e7.6. Small-Sample Ordinal Tests of Independence.\u003c\/p\u003e \u003cp\u003e7.7. Other Rank-Based Statistical Methods for Ordered Categories.\u003c\/p\u003e \u003cp\u003eAppendix: Standard Errors for Ordinal Measures.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Matched-Pairs Data with Ordered Categories.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. Comparing Marginal Distributions for Matched Pairs.\u003c\/p\u003e \u003cp\u003e8.2. Models Comparing Matched Marginal Distributions.\u003c\/p\u003e \u003cp\u003e8.3. Models for The Joint Distribution in A Square Table.\u003c\/p\u003e \u003cp\u003e8.4. Comparing Marginal Distributions for Matched Sets.\u003c\/p\u003e \u003cp\u003e8.5. Analyzing Rater Agreement on an Ordinal Scale.\u003c\/p\u003e \u003cp\u003e8.6. Modeling Ordinal Paired Preferences.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Clustered Ordinal Responses: Marginal Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1. Marginal Ordinal Modeling with Explanatory Variables.\u003c\/p\u003e \u003cp\u003e9.2. Marginal Ordinal Modeling: GEE Methods.\u003c\/p\u003e \u003cp\u003e9.3. Transitional Ordinal Modeling, Given the Past.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Clustered Ordinal Responses: Random Effects Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1. Ordinal Generalized Linear Mixed Models.\u003c\/p\u003e \u003cp\u003e10.2. Examples of Ordinal Random Intercept Models.\u003c\/p\u003e \u003cp\u003e10.3. Models with Multiple Random Effects.\u003c\/p\u003e \u003cp\u003e10.4. Multilevel (Hierarchical) Ordinal Models.\u003c\/p\u003e \u003cp\u003e10.5. Comparing Random Effects Models and Marginal Models.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Bayesian Inference for Ordinal Response Data.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1. Bayesian Approach to Statistical Inference.\u003c\/p\u003e \u003cp\u003e11.2. Estimating Multinomial Parameters.\u003c\/p\u003e \u003cp\u003e11.3. Bayesian Ordinal Regression Modeling.\u003c\/p\u003e \u003cp\u003e11.4. Bayesian Ordinal Association Modeling.\u003c\/p\u003e \u003cp\u003e11.5. Bayesian Ordinal Multivariate Regression Modeling.\u003c\/p\u003e \u003cp\u003e11.6. Bayesian Versus Frequentist Approaches to Analyzing Ordinal Data.\u003c\/p\u003e \u003cp\u003eChapter Notes.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix Software for Analyzing Ordinal Categorical Data.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBibliography.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eExample Index.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSubject Index.\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864622838103,"sku":"9780470082898","price":113.36,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470082898.jpg?v=1722272774"},{"product_id":"vector-and-tensor-analysis-with-applications-9780486638331","title":"Vector and Tensor Analysis with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864739459415,"sku":"9780486638331","price":13.04,"currency_code":"GBP","in_stock":true}]},{"product_id":"quantitative-risk-management-9780691166278","title":"Quantitative Risk Management","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of the Top 10 Technical Books on Financial Engineering by Financial Engineering News for 2006 Praise for the previous edition: \"This book provides a state-of-the-art discussion of the three main categories of risk in financial markets, market risk, ... credit risk ... and operational risk... This is a high level, but well-written treatment, rigorous (sometimes succinct), complete with theorems and proofs.\"--D.L. McLeish, Short Book Reviews of the International Statistical Institute Praise for the previous edition: \"A great summary of the latest techniques available within quantitative risk measurement... [I]t is an excellent text to have on the shelf as a reference when your day job covers the whole spectrum of quantitative techniques in risk management.\"--Financial Engineering News Praise for the previous edition: \"Alexander McNeil, Rudiger Frey and Paul Embrechts have written a beautiful book... [T]here is no book that can provide the type of rigorous, detailed, well balanced and relevant coverage of quantitative risk management topics that Quantitative Risk Management: Concepts, Techniques, and Tools offers... I believe that this work may become the book on quantitative risk management... [N]o book that I know of can provide better guidance.\"--Dr. Riccardo Rebonato, Global Association of Risk Professionals (GARP) Review Praise for the previous edition: \"This is a very impressive book on a rapidly growing field. It certainly helps to discover the forest in an area where a lot of trees are popping up daily.\"--Hans Buhlmann, SIAM Review Praise for the previous edition: \"This book is a compendium of the statistical arrows that should be in any quantitative risk manager's quiver. It includes extensive discussion of dynamic volatility models, extreme value theory, copulas and credit risk. Academics, PhD students and quantitative practitioners will find many new and useful results in this important volume.\"--Robert F. Engle III, 2003 Nobel Laureate in Economic Sciences, Michael Armellino Professor in the Management of Financial Services at New York University's Stern School of Business Praise for the previous edition: \"Quantitative Risk Management can be highly recommended to anyone looking for an excellent survey of the most important techniques and tools used in this rapidly growing field.\"--Holger Drees, Risk Praise for the previous edition: \"Quantitative Risk Management is highly recommended for financial regulators. The statistical and mathematical tools facilitate a better understanding of the strengths and weaknesses of a useful range of advanced risk-management concepts and models, while the focus on aggregate risk enhances the publication's value to banking and insurance supervisors.\"--Hans Blommestein, Financial Regulator Praise for the previous edition: \"This book provides a framework and a useful toolkit for analysis of a wide variety of risk management problems. Common pitfalls are pointed out, and mathematical sophistication is used in pursuit of useful and usable solutions. Every financial institution has a risk management department that looks at aggregated portfolio-wide risks on longer time scales, and at risk exposure to large, or extreme, market movements. Risk managers are always on the lookout for good techniques to help them do their jobs. This very good book provides these techniques and addresses an important, and under-developed, area of practical research.\"--Martin Baxter, Nomura International","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865532248407,"sku":"9780691166278","price":80.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691166278.jpg?v=1722274423"},{"product_id":"positive-definite-matrices-9780691168258","title":"Positive Definite Matrices","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical enginee\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Written by an expert in the area, the book presents in an accessible manner a lot of important results from the realm of positive matrices and of their applications... The book can be used for graduate courses in linear algebra, or as supplementary material for courses in operator theory, and as a reference book by engineers and researchers working in the applied field of quantum information.\"--S. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica \"There is no obvious competitor for Bhatia's book, due in part to its focus, but also because it contains some very recent material drawn from research articles. Beautifully written and intelligently organised, Positive Definite Matrices is a welcome addition to the literature. Readers who admired his Matrix Analysis will no doubt appreciate this latest book of Rajendra Bhatia.\"--Douglas Farenick, Image \"This is an outstanding book. Its exposition is both concise and leisurely at the same time.\"--Jaspal Singh Aujla, Zentralblatt MATH\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii     Chapter 1: Positive Matrices 1  1.1 Characterizations 1  1.2 Some Basic Theorems 5  1.3 Block Matrices 12  1.4 Norm of the Schur Product 16  1.5 Monotonicity and Convexity 18  1.6 Supplementary Results and Exercises 23  1.7 Notes and References 29      Chapter 2: Positive Linear Maps 35  2.1 Representations 35  2.2 Positive Maps 36  2.3 Some Basic Properties of Positive Maps 38  2.4 Some Applications 43  2.5 Three Questions 46  2.6 Positive Maps on Operator Systems 49  2.7 Supplementary Results and Exercises 52  2.8 Notes and References 62      Chapter 3: Completely Positive Maps 65  3.1 Some Basic Theorems 66  3.2 Exercises 72  3.3 Schwarz Inequalities 73  3.4 Positive Completions and Schur Products 76  3.5 The Numerical Radius 81  3.6 Supplementary Results and Exercises 85  3.7 Notes and References 94      Chapter 4: Matrix Means 101  4.1 The Harmonic Mean and the Geometric Mean 103  4.2 Some Monotonicity and Convexity Theorems 111  4.3 Some Inequalities for Quantum Entropy 114  4.4 Furuta's Inequality 125  4.5 Supplementary Results and Exercises 129  4.6 Notes and References 136      Chapter 5: Positive Definite Functions 141  5.1 Basic Properties 141  5.2 Examples 144  5.3 Loewner Matrices 153  5.4 Norm Inequalities for Means 160  5.5 Theorems of Herglotz and Bochner 165  5.6 Supplementary Results and Exercises 175  5.7 Notes and References 191      Chapter 6: Geometry of Positive Matrices 201  6.1 The Riemannian Metric 201  6.2 The Metric Space Pn 210  6.3 Center of Mass and Geometric Mean 215  6.4 Related Inequalities 222  6.5 Supplementary Results and Exercises 225  6.6 Notes and References 232      Bibliography 237  Index 247  Notation 253","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865533296983,"sku":"9780691168258","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"the-golden-ticket-9780691175782","title":"The Golden Ticket","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Amazon.com's 2013 Best Science Books One of Choice's Outstanding Academic Titles for 2013 Honorable Mention for the 2013 PROSE Award in Popular Science \u0026amp; Mathematics, Association of American Publishers \"As Fortnow describes... P versus NP is 'one of the great open problems in all of mathematics' not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, 'from cures to deadly diseases to the nature of the universe,' even 'an algorithmic process to recognize greatness.'... To postulate that P ? NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration--but also of discovery and inquiry, of pleasures pleasingly delayed.\"--Alexander Nazaryan, New Yorker \"Fortnow effectively initiates readers into the seductive mystery and importance of P and NP problems.\"--Publishers Weekly \"Fortnow's book is just the ticket for bringing one of the major theoretical problems of our time to the level of the average citizen--and yes, that includes elected officials.\"--Veit Elser, Science \"Without bringing formulas or computer code into the narrative, Fortnow sketches the history of this class of questions, convincingly demonstrates their surprising equivalence, and reveals some of the most far-reaching implications that a proof of P = NP would bring about. These might include tremendous advances in biotechnology (for instance, more cures for cancer), information technology, and even the arts. Verdict: Through story and analogy, this relatively slim volume manages to provide a thorough, accessible explanation of a deep mathematical question and its myriad consequences. An engaging, informative read for a broad audience.\"--J.J.S. Boyce, Library Journal \"A provocative reminder of the real-world consequences of a theoretical enigma.\"--Booklist \"The definition of this problem is tricky and technical, but in The Golden Ticket, Lance Fortnow cleverly sidesteps the issue with a boiled-down version. P is the collection of problems we can solve quickly, NP is the collection of problems we would like to solve. If P = NP, computers can answer all the questions we pose and our world is changed forever. It is an oversimplification, but Fortnow, a computer scientist at Georgia Institute of Technology, Atlanta, knows his stuff and aptly illustrates why NP problems are so important.\"--Jacob Aron, New Scientist \"Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science.\"--Rob Hardy, Commercial Dispatch \"A great book... [Lance Fortnow] has written precisely the book about P vs. NP that the interested layperson or IT professional wants and needs.\"--Scott Aaronson, Shtetl-Optimized blog \"[The Golden Ticket] is a book on a technical subject aimed at a general audience... Lance's mix of technical accuracy with evocative story telling works.\"--Michael Trick, Michael Trick's Operations Research Blog \"Thoroughly researched and reviewed. Anyone from a smart high school student to a computer scientist is sure to get a lot of this book. The presentation is beautiful. There are few formulas but lots of facts.\"--Daniel Lemire's Blog \"An entertaining discussion of the P versus NP problem.\"--Andrew Binstock, Dr. Dobb's \"The Golden Ticketis an extremely accessible and enjoyable treatment of the most important question of theoretical computer science, namely whether P is equal to NP.\"--Choice \"The book is accessible and useful for practically anyone from smart high school students to specialists... [P]erhaps the interest sparked by this book will be the 'Golden Ticket' for further accessible work in this area. And perhaps P=NP will start to become as famous as E=mc2.\"--Michael Trick, INFORMS Journal of Computing \"In any case, it is excellent to have a nontechnical book about the P versus NP question. The Golden Ticket offers an inspiring introduction for nontechnical readers to what is surely the most important open problem in computer science.\"--Leslie Ann Goldberg, LMS Newsletter \"The Golden Ticket does a good job of explaining a complex concept in terms that a secondary-school student will understand--a hard problem in its own right, even if not quite NP.\"--Physics World \"[The Golden Ticket] is fun to read and can be fully appreciated without any knowledge in (theoretical) computer science. Fortnow's efforts to make the difficult material accessible to non-experts should be commended.\"--Andreas Maletti, Zentralblatt MATH \"This is a fabulous book for both educators and students at the secondary school level and above. It does not require any particular mathematical knowledge but, rather, the ability to think. Enjoy the world of abstract ideas as you experience an intriguing journey through mathematical thinking.\"--Gail Kaplan, Mathematics Teacher \"Fortnow's book provides much of the background and personal information on the main characters involved in this problem--notably Steven Cook, with a cameo appearance by Kurt Godel--that one does not get in the more technical treatments. There is a lot of information in this book, and the serious computer science student is sure to learn from it.\"--James M. Cargal, UMAP Journal\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix Chapter 1 The Golden Ticket 1 Chapter 2 The Beautiful World 11 Chapter 3 P and NP 29 Chapter 4 The Hardest Problems in NP 51 Chapter 5 The Prehistory of P versus NP 71 Chapter 6 Dealing with Hardness 89 Chapter 7 Proving P \u0026lt;\u0026gt; NP 109 Chapter 8 Secrets 123 Chapter 9 Quantum 143 Chapter 10 The Future 155 Acknowledgments 163 Chapter Notes and Sources 165 Index 171","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537032535,"sku":"9780691175782","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"how-to-fall-slower-than-gravity-9780691176918","title":"How to Fall Slower Than Gravity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book is without a doubt the most enjoyable, stimulating book of mathematical physics (and occasionally more pure branches of maths) puzzles that I have ever read. It’s essentially a series of cleverly, and occasionally fiendishly put-together mathematics and physics challenge questions, each of which gets you thinking in a new and fascinating way.\"\u003cb\u003e---Jonathan Shock, \u003ci\u003eMathemafrica\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Reading Nahin is like reading through a select library of ancient Babylonian mathematical clay tablets. Surprises abound. . . . Nahin weaves much colorful history into his narrative.\"\u003cb\u003e---Andrew Simoson, \u003ci\u003eMathematical Intelligencer\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Engaging. . . . The book contains a wealth of original problems. . . . An enjoyable read.\"\u003cb\u003e---Antonín Slavík, \u003ci\u003eZentralblatt MATH\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This reviewer found himself being drawn to a variety of unfamiliar settings with much interest and even fascination.\" * Choice *\u003cbr\u003e\"I certainly enjoyed [the book]!\"\u003cb\u003e---Alan Stevens, \u003ci\u003eMathematics Today\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"The potential audience for this book should be fairly large and go from highly talented high school students up through professionals in any STEM field.\"\u003cb\u003e---Geoffrey Dietz, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537950039,"sku":"9780691176918","price":19.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691176918.jpg?v=1722274452"},{"product_id":"ti84-plus-ce-graphing-calculator-for-dummies-9781119887607","title":"TI84 Plus CE Graphing Calculator 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\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 1: Making Friends with the Calculator\u003c\/b\u003e\u003cb\u003e 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1: Starting with the Basics 7\u003c\/p\u003e \u003cp\u003eChapter 2: Doing Basic Arithmetic 25\u003c\/p\u003e \u003cp\u003eChapter 3: Dealing with Fractions 35\u003c\/p\u003e \u003cp\u003eChapter 4: Solving Equations 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 2: Taking Your Calculator Relationship to the Next Level\u003c\/b\u003e\u003cb\u003e 53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 5: Working with Complex Numbers 55\u003c\/p\u003e \u003cp\u003eChapter 6: Understanding the Math Menu and Submenus 61\u003c\/p\u003e \u003cp\u003eChapter 7: The Angle and Test Menus 69\u003c\/p\u003e \u003cp\u003eChapter 8: Creating and Editing Matrices 79\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 3: Graphing and Analyzing Functions\u003c\/b\u003e\u003cb\u003e 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 9: Graphing Functions 91\u003c\/p\u003e \u003cp\u003eChapter 10: Exploring Functions 111\u003c\/p\u003e \u003cp\u003eChapter 11: Evaluating Functions 127\u003c\/p\u003e \u003cp\u003eChapter 12: Graphing Inequalities 143\u003c\/p\u003e \u003cp\u003eChapter 13: Graphing Parametric Equations 155\u003c\/p\u003e \u003cp\u003eChapter 14: Graphing Polar Equations 163\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 4: Working with Probability and Statistics\u003c\/b\u003e\u003cb\u003e 173\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 15: Probability 175\u003c\/p\u003e \u003cp\u003eChapter 16: Dealing with Statistical Data 183\u003c\/p\u003e \u003cp\u003eChapter 17: Analyzing Statistical Data 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 5: Doing More with Your Calculator\u003c\/b\u003e\u003cb\u003e 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 18: Communicating with a PC Using TI Connect CE Software 211\u003c\/p\u003e \u003cp\u003eChapter 19: Communicating Between Calculators 221\u003c\/p\u003e \u003cp\u003eChapter 20: Fun with Images 227\u003c\/p\u003e \u003cp\u003eChapter 21: Managing Memory 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 6: The Part of Tens\u003c\/b\u003e\u003cb\u003e 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 22: Ten Essential Skills 239\u003c\/p\u003e \u003cp\u003eChapter 23: Ten Common Errors 243\u003c\/p\u003e \u003cp\u003eChapter 24: Ten Common Error Messages 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 7: Appendices\u003c\/b\u003e\u003cb\u003e 253\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix A: Creating Calculator Programs 255\u003c\/p\u003e \u003cp\u003eAppendix B: Controlling Program Input and Output 259\u003c\/p\u003e \u003cp\u003eAppendix C: Controlling Program Flow 269\u003c\/p\u003e \u003cp\u003eAppendix D: Introducing Python Programming 281\u003c\/p\u003e \u003cp\u003eAppendix E: Mastering the Basics of Python Programming 287\u003c\/p\u003e \u003cp\u003eIndex 293\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48866423177559,"sku":"9781119887607","price":18.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119887607.jpg?v=1722278574"},{"product_id":"how-to-analyze-data-pocket-study-skills-9781137608468","title":"How to Analyze Data Pocket Study Skills","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eCatrin Radcliffe\u003c\/b\u003e is a tutor of mathematics and statistics at Oxford Brookes University, UK.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction  PART 1: GETTING STARTED  1. What does your assignment ask you to do?  2. How will you do it?  3. Defining your research question  4. Tips for designing your questionnaire  5. How to enter your data into a spreadsheet  PART 2: UNDERSTANDING AND DESCRIBING YOUR DATA  6. What type of data do you have?  7. Descriptive statistics  8. What plot should you use?  PART 3: HOW DO STATISTICAL TESTS WORK?  9. What is a statistical hypothesis?  10. Using probability distributions in statistical tests  11. Statistics, \"errors\" and interpretation  PART 4: WHAT STATISTICAL TEST DO YOU NEED?  12. The statistics signpost  13. Statistical flowcharts  14. Case studies  PART 5: THE STATISTICAL PROCESS  15. You the researcher  16. You the interpreter  Symbols explained  Useful resources  References  Index.","brand":"Bloomsbury Publishing PLC","offers":[{"title":"Default Title","offer_id":48866429501783,"sku":"9781137608468","price":10.13,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781137608468.jpg?v=1722278605"},{"product_id":"numerical-analysis-9781305253667","title":"Numerical Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burden's NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software and Chapter Summary. 2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE. The Bisection Method. Fixed-Point Iteration. Newton's Method and Its Extensions. Error Analysis for Iterative Methods. Accelerating Convergence. Zeros of Polynomials and M��ller's Method. Numerical Software and Chapter Summary. 3. INTERPOLATION AND POLYNOMIAL APPROXIMATION. Interpolation and the Lagrange Polynomial. Data Approximation and Neville's Method. Divided Differences. Hermite Interpolation. Cubic Spline Interpolation. Parametric Curves. Numerical Software and Chapter Summary. 4. NUMERICAL DIFFERENTIATION AND INTEGRATION. Numerical Differentiation. Richardson's Extrapolation. Elements of Numerical Integration. Composite Numerical Integration. Romberg Integration. Adaptive Quadrature Methods. Gaussian Quadrature. Multiple Integrals. Improper Integrals. Numerical Software and Chapter Summary. 5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Elementary Theory of Initial-Value Problems. Euler's Method. Higher-Order Taylor Methods. Runge-Kutta Methods. Error Control and the Runge-Kutta-Fehlberg Method. Multistep Methods. Variable Step-Size Multistep Methods. Extrapolation Methods. Higher-Order Equations and Systems of Differential Equations. Stability. Stiff Differential Equations. Numerical Software and Chapter Summary. 6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS. Linear Systems of Equations. Pivoting Strategies. Linear Algebra and Matrix Inversion. The Determinant of a Matrix. Matrix Factorization. Special Types of Matrices. Numerical Software and Chapter Summary. 7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA. Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Numerical Software and Chapter Summary. 8. APPROXIMATION THEORY. Discrete Least Squares Approximation. Orthogonal Polynomials and Least Squares Approximation. Chebyshev Polynomials and Economization of Power Series. Rational Function Approximation. Trigonometric Polynomial Approximation. Fast Fourier Transforms. Numerical Software and Chapter Summary. 9. APPROXIMATING EIGENVALUES. Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method. The QR Algorithm. Singular Value Decomposition. Numerical Software and Chapter Summary. 10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS. Fixed Points for Functions of Several Variables. Newton's Method. Quasi-Newton Methods. Steepest Descent Techniques. Homotopy and Continuation Methods. Numerical Software and Chapter Summary. 11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Linear Shooting Method. The Shooting Method for Nonlinear Problems. Finite-Difference Methods for Linear Problems. Finite-Difference Methods for Nonlinear Problems. The Rayleigh-Ritz Method. Numerical Software and Chapter Summary. 12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS. Elliptic Partial Differential Equations. Parabolic Partial Differential Equations. Hyperbolic Partial Differential Equations. An Introduction to the Finite-Element Method. Numerical Software and Chapter Summary. Bibliography. Answers to Selected Exercises.","brand":"Cengage Learning, Inc","offers":[{"title":"Default Title","offer_id":48866548416855,"sku":"9781305253667","price":77.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781305253667.jpg?v=1722279174"},{"product_id":"physics-for-scientists-and-engineers-with-modern-physics-9781337553292","title":"Physics for Scientists and Engineers with Modern","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I: MECHANICS. 1. Physics and Measurement. 2. Motion in One Dimension. 3. Vectors. 4. Motion in Two Dimensions. 5. The Laws of Motion. 6. Circular Motion and Other Applications of Newton's Laws. 7. Energy of a System. 8. Conservation of Energy. 9. Linear Momentum and Collisions. 10. Rotation of a Rigid Object About a Fixed Axis. 11. Angular Momentum. 12. Static Equilibrium and Elasticity. 13. Universal Gravitation. 14. Fluid Mechanics. Part II: OSCILLATIONS AND MECHANICAL WAVES. 15. Oscillatory Motion. 16. Wave Motion. 17. Superposition and Standing Waves. Part III: THERMODYNAMICS. 18. Temperature. 19. Heat and the First Law of Thermodynamics. 20. The Kinetic Theory of Gases. 21. Heat Engines, Entropy, and the Second Law of Thermodynamics. Part IV: ELECTRICITY AND MAGNETISM. 22. Electric Fields. 23. Continuous Charge Distributions and Gauss's Law. 24. Electric Potential. 25. Capacitance and Dielectrics. 26. Current and Resistance. 27. Direct Current Circuits. 28. Magnetic Fields. 29. Sources of the Magnetic Field. 30. Faraday's Law. 31. Inductance. 32. Alternating Current Circuits. 33. Electromagnetic Waves. Part V: LIGHT AND OPTICS. 34. The Nature of Light and the Laws of Geometric Optics. 35. Image Formation. 36. Interference of Light Waves. 37. Diffraction Patterns and Polarization. Part VI: MODERN PHYSICS. 38. Relativity. 39. Introduction to Quantum Physics. 40. Quantum Mechanics. 41. Atomic Physics. 42. Molecules and Solids. 43. Nuclear Physics. 44. Particle Physics and Cosmology. APPENDICES. A. Tables. B. Mathematics Review. C. Periodic Table of the Elements. D. SI Units. Answers to Quick Quizzes and Odd-Numbered Problems. Index.","brand":"Cengage Learning, Inc","offers":[{"title":"Default Title","offer_id":48866571747671,"sku":"9781337553292","price":76.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781337553292.jpg?v=1722279271"},{"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":"understanding-analysis-9781493927111","title":"Understanding Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAcutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The choice of topics is a happy combination of the essential and the interesting, all truly leading to an understanding of what analysis is and what questions it addresses, aided by the author’s extraordinarily lucid exposition. … Summing Up: Highly recommended. Upper-division undergraduates.” (D. Robbins, Choice, Vol. 53 (2), October, 2015)\u003c\/p\u003e\u003cp\u003e“This is the second edition of a text for an undergraduate course in single-variable real analysis. … The topics covered in this book are the ones that have, by now, become standard for a one-semester undergraduate real analysis course … . Overall, this book represents, to my mind, the gold standard among single-variable undergraduate analysis texts.” (Mark Hunacek, MAA Reviews, June, 2015)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“This is a dangerous book. \u003ci\u003eUnderstanding Analysis\u003c\/i\u003e is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. … \u003ci\u003eUnderstanding Analysis\u003c\/i\u003e is perfectly titled; if your students read it, that’s what’s going to happen. This terrific book will become the text of choice for the single-variable introductory analysis course; take a look at it next time you’re preparing that class.”\u003c\/p\u003e\u003cp\u003e— Steve Kennedy, \u003cb\u003eMAA Reviews\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e“Each chapter begins with a discussion section and ends with an epilogue. The discussion serves to motivate the content of the chapter while the epilogue points tantalisingly to more advanced topics. … I wish I had written this book! The development of the subject follows the tried-and-true path, but the presentation is engaging and challenging. Abbott focuses attention immediately on the topics which make analysis fascinating … and makes them accessible to an inexperienced audience.”\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e— Scott Sciffer, \u003cb\u003eThe Australian Mathem\u003c\/b\u003eatical Society Gazette             \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.            ","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48867321315671,"sku":"9781493927111","price":31.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781493927111.jpg?v=1722282782"},{"product_id":"grundwissen-mathematikstudium-analysis-und-lineare-algebra-mit-querverbindungen-analysis-und-lineare-algebra-mit-querverbindungen-9783662633120","title":"Grundwissen Mathematikstudium – Analysis und","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDieses vierfarbige Lehrbuch wendet sich an Studierende der Mathematik in Bachelor- und Lehramts-Studiengängen. Es bietet in einem Band ein lebendiges Bild der mathematischen Inhalte, die üblicherweise im ersten Studienjahr behandelt werden (und etliches mehr). \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eMathematik-Studierende finden wichtige Begriffe, Sätze und Beweise ausführlich und mit vielen Beispielen erklärt und werden an grundlegende Konzepte und Methoden herangeführt.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIm Mittelpunkt stehen das Verständnis der mathematischen Zusammenhänge und des Aufbaus der Theorie sowie die Strukturen und Ideen wichtiger Sätze und Beweise. Es wird nicht nur ein in sich geschlossenes Theoriengebäude dargestellt, sondern auch verdeutlicht, wie es entsteht und wozu die Inhalte später benötigt werden.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eHerausragende Merkmale sind\u003c\/b\u003e:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- durchgängig vierfarbiges Layout mit mehr als 600 Abbildungen\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- prägnant formulierte Kerngedanken bilden die Abschnittsüberschriften\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- Selbsttests in kurzen Abständen ermöglichen Lernkontrollen während des Lesens\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- farbige Merkkästen heben das Wichtigste hervor\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- „Unter-der-Lupe“-Boxen zoomen in Beweise hinein, motivieren und erklären Details\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- „Hintergrund-und-Ausblick“-Boxen  stellen Zusammenhänge zu anderen Gebieten und weiterführenden Themen her\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- Zusammenfassungen zu jedem Kapitel sowie Übersichtsboxen\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- mehr als 400 Verständnisfragen, Rechenaufgaben und Aufgaben zu Beweisen\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e- deutsch-englisches Symbol- und Begriffsglossar \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eDer inhaltliche Schwerpunkt liegt auf den Themen der Vorlesungen Analysis 1 und 2 sowie  Linearer Algebra 1 und 2. Behandelt werden darüber hinaus Inhalte und Methodenkompetenzen, die vielerorts im ersten Studienjahr der Mathematikausbildung vermittelt werden.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eHinweise, Lösungswege und Ergebnisse zu allen Aufgaben des Buchs stehen als PDF-Dateien auf http:\/\/sn.pub\/extras in dem Ordner für das Werk Arens et al, „Mathematik“, Copyrightjahr 2018 zur Verfügung. \u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eDas Buch wird allen Studierenden der Mathematik vom Beginn des Studiums bis in höhere Semester hinein ein verlässlicher Begleiter sein.\u003c\/p\u003e\u003cp\u003eFür die 2. Auflage ist es vollständig durchgesehen, an zahlreichen Stellen didaktisch weiter verbessert und um einige Themen ergänzt worden.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eStimme zur ersten Auflage:\u003cbr\u003e\u003c\/b\u003e„Besonders gut gefallen mir die Übersichtlichkeit und die Verständlichkeit, besonders aber die Sichtbarmachung der Verbindung von Analysis und linearer Algebra, die in den Erstsemestervorlesungen oft zu kurz kommt.” \u003ci\u003eSylvia Prinz, Institut für Mathematikdidaktik, Universität zu Köln\u003c\/i\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eVorwort.- \u003cb\u003e1 Was ist Mathematik und was tun Mathematiker?\u003c\/b\u003e- \u003cb\u003e2 Logik, Mengen, Abbildungen − die Sprache der Mathematik\u003c\/b\u003e.- 2.1 Junktoren und Quantoren.- 2.2 Grundbegriffe aus der Mengenlehre.- 2.3 Abbildungen.- 2.4 Relationen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e3 Algebraische Strukturen − ein Blick hinter die Rechenregeln\u003c\/b\u003e.- 3.1 Gruppen.- 3.2 Homomorphismen.- 3.3 Körper.- 3.4 Ringe.- Zusammenfassung.- Aufgaben.- \u003cb\u003e4 Zahlbereiche − Basis nicht nur der Analysis\u003c\/b\u003e.- 4.1 Reelle Zahlen.- 4.2 Körperaxiome für die reellen Zahlen.- 4.3 Anordnungsaxiome für die reellen Zahlen.- 4.4 Ein Vollständigkeitsaxiom für die reellen Zahlen.- 4.5 Natürliche Zahlen und vollständige Induktion.- 4.6 Ganze Zahlen und rationale Zahlen.- 4.7 Komplexe Zahlen: Ihre Arithmetik und Geometrie.- Zusammenfassung.- Aufgaben.- \u003cb\u003e5 Lineare Gleichungssysteme − \u003c\/b\u003e\u003cb\u003eein Tor zur\u003c\/b\u003e \u003cb\u003elinearen Algebra\u003c\/b\u003e.- 5.1 Erste Lösungsversuche.- 5.2 Das Lösungsverfahren von Gauß und Jordan.- 5.3 Das Lösungskriterium und die Struktur der Lösung.- Zusammenfassung.- Aufgaben.- \u003cb\u003e6 Vektorräume − von Basen und Dimensionen\u003c\/b\u003e.- 6.1 Der Vektorraumbegriff.- 6.2 Beispiele von Vektorräumen.- 6.3 Untervektorräume.- 6.4 Basis und Dimension.- 6.5 Summe und Durchschnitt von Untervektorräumen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e7 Analytische Geometrie − Rechnen statt Zeichnen\u003c\/b\u003e.- 7.1 Punkte und Vektoren im Anschauungsraum.- 7.2 Das Skalarprodukt im Anschauungsraum.- 7.3 Weitere Produkte von Vektoren im Anschauungsraum.- 7.4 Abstände zwischen Punkten, Geraden und Ebenen.- 7.5 Wechsel zwischen kartesischen Koordinatensystemen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e8 Folgen − der Weg ins Unendliche\u003c\/b\u003e.- 8.1 Der Begriff einer Folge.- 8.2 Konvergenz.- 8.3 Häufungspunkte und Cauchy-Folgen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e9 Funktionen und Stetigkeit − ε trifft auf δ\u003c\/b\u003e.- 9.1 Grundlegendes zu Funktionen.- 9.2 Beschränkte und monotone Funktionen.- 9.3 Grenzwerte für Funktionen und die Stetigkeit.- 9.4 Abgeschlossene, offene, kompakte Mengen.- 9.5 Stetige Funktionen mit kompaktem Definitionsbereich, Zwischenwertsatz.- Zusammenfassung.- Aufgaben.- \u003cb\u003e10 Reihen − Summieren bis zum Letzten\u003c\/b\u003e.- 10.1 Motivation und Definition.- 10.2 Kriterien für Konvergenz.- 10.3 Absolute Konvergenz.- 10.4 Kriterien für absolute Konvergenz.- Zusammenfassung.- Aufgaben.- \u003cb\u003e11 Potenzreihen − Alleskönner unter den Funktionen\u003c\/b\u003e.- 11.1 Definition und Grundlagen.- 11.2 Die Darstellung von Funktionen durch Potenzreihen.- 11.3 Die Exponentialfunktion.- 11.4 Trigonometrische Funktionen.- 11.5 Der Logarithmus.- Zusammenfassung.- Aufgaben.- \u003cb\u003e12 Lineare Abbildungen und Matrizen − Brücken zwischen Vektorräumen\u003c\/b\u003e.- 12.1 Definition und Beispiele.- 12.2 Verknüpfungen von linearen Abbildungen.- 12.3 Kern, Bild und die Dimensionsformel.- 12.4 Darstellungsmatrizen.- 12.5 Das Produkt von Matrizen.- 12.6 Das Invertieren von Matrizen.- 12.7 Elementarmatrizen.- 12.8 Basistransformation.- 12.9 Der Dualraum.- Zusammenfassung.- Aufgaben.- \u0026lt;13 Determinanten − Kenngrößen von Matrizen.- 13.1 Die Definition der Determinante.- 13.2 Determinanten von Endomorphismen.- 13.3 Berechnung der Determinante.- 13.4 Anwendungen der Determinante.- Zusammenfassung.- Aufgaben.- \u003cb\u003e14 Normalformen − Diagonalisieren und Triangulieren\u003c\/b\u003e.- 14.1 Diagonalisierbarkeit.- 14.2 Eigenwerte und Eigenvektoren.- 14.3 Berechnung der Eigenwerte und Eigenvektoren.- 14.4 Algebraische und geometrische Vielfachheit.- 14.5 Die Exponentialfunktion für Matrizen.- 14.6 Das Triangulieren von Endomorphismen.- 14.7 Die Jordan-Normalform.- 14.8 Die Berechnung einer Jordan-Normalform und Jordan-Basis.- Zusammenfassung.- Aufgaben.- \u003cb\u003e15 Differenzialrechnung − die Linearisierung von Funktionen\u003c\/b\u003e.- 15.1 Die Ableitung.- 15.2 Differenziationsregeln.- 15.3 Der Mittelwertsatz.- 15.4 Verhalten differenzierbarer Funktionen.- 15.5 Taylorreihen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e16 Integrale − von lokal zu global\u003c\/b\u003e.- 16.1 Integration von Treppenfunktionen.- 16.2 Das Lebesgue-Integral.- 16.3 Stammfunktionen.- 16.4 Integrationstechniken.- 16.5 Integration über unbeschränkte Intervalle oder Funktionen.- 16.6 Parameterabhängige Integrale.- 16.7 Weitere Integrationsbegriffe.- Zusammenfassung.- Aufgaben.- \u003cb\u003e17 Euklidische und unitäre Vektorräume − orthogonales Diagonalisieren\u003c\/b\u003e.- 17.1 Euklidische Vektorräume.- 17.2 Norm, Abstand, Winkel, Orthogonalität.- 17.3 Orthonormalbasen und orthogonale Komplemente.- 17.4 Unitäre Vektorräume.- 17.5 Orthogonale und unitäre Endomorphismen.- 17.6 Selbstadjungierte Endomorphismen.- 17.7 Normale Endomorphismen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e18 Quadriken − vielseitig nutzbare Punktmengen\u003c\/b\u003e.- 18.1 Symmetrische Bilinearformen.- 18.2 Hermitesche Sesquilinearformen.- 18.3 Quadriken und ihre Hauptachsentransformation.- 18.4 Die Singulärwertzerlegung.- 18.5 Die Pseudoinverse einer linearen Abbildung.- Zusammenfassung.- Aufgaben.- \u003cb\u003e19 Funktionenräume − Analysis und lineare Algebra Hand in Hand\u003c\/b\u003e.- 19.1 Metrische Räume und ihre Topologie, normierte Räume.- 19.2 Konvergenz und Stetigkeit in metrischen Räumen.- 19.3 Kompaktheit.- 19.4 Zusammenhangsbegriffe.- 19.5 Vollständigkeit.- 19.6 Banach- und Hilberträume.- Zusammenfassung.- Aufgaben.- \u003cb\u003e20 Differenzialgleichungen − Funktionen sind gesucht\u003c\/b\u003e.- 20.1 Begriffsbildungen.- 20.2 Elementare analytische Techniken.- 20.3 Existenz und Eindeutigkeit.- 20.4 Grundlegende numerische Verfahren.- Zusammenfassung.- Aufgaben .- \u003cb\u003e21 Funktionen mehrerer Variablen − Differenzieren im Raum\u003c\/b\u003e.- 21.1 Einführung.- 21.2 Differenzierbarkeitsbegriffe: Totale und partielle Differenzierbarkeit.- 21.3 Differenziationsregeln.- 21.4 Mittelwertsätze und Schranksätze.- 21.5 Höhere partielle Ableitungen und der der Vertauschungssatz von H. A. Schwarz.- 21.6 Taylor-Formel und lokale Extrema.- 21.7 Der Lokale Umkehrsatz.- 21.8 Der Satz über implizite Funktionen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e22 Gebietsintegrale − das Ausmessen von Mengen\u003c\/b\u003e.- 22.1 Definition und Eigenschaften.- 22.2 Die Berechnung von Integralen.- 22.3 Die Transformationsformel.- 22.4 Wichtige Koordinatensysteme.- Zusammenfassung.- Aufgaben.- \u003cb\u003e23 Vektoranalysis − im Zentrum steht der Gauß'sche Satz\u003c\/b\u003e.- 23.1 Kurven und Kurvenintegrale.- 23.2 Flächen und Flächenintegrale.- 23.3 Der Gauß’sche Satz.- Zusammenfassung.- Aufgaben.- \u003cb\u003e24 Optimierung − ein sehr generelles Problem\u003c\/b\u003e.- 24.1 Lineare Optimierung.- 24.2 Das Simplex-Verfahren.- 24.3 Dualitätstheorie.- Zusammenfassung.- Aufgaben.- \u003cb\u003e25 Elementare Zahlentheorie − Teiler und Vielfache\u003c\/b\u003e.- 25.1 Teilbarkeit.- 25.2 Der euklidische Algorithmus.- 25.3 Der Fundamentalsatz der Arithmetik.- 25.4 ggT und kgV.- 25.5 Zahlentheoretische Funktionen.- 25.6 Rechnen mit Kongruenzen.- Zusammenfassung.- Aufgaben.- \u003cb\u003e26 Elemente der diskreten Mathematik − die Kunst des Zählens\u003c\/b\u003e.- 26.1 Einführung in die Graphentheorie.- 26.2 Einführung in die Kombinatorik.- 26.3 Erzeugende Funktionen.- Zusammenfassung.- Aufgaben.- Hinweise zu den Aufgaben.- Lösungen zu den Aufgaben.- Symbolglossar.- Index.","brand":"Springer Fachmedien Wiesbaden","offers":[{"title":"Default Title","offer_id":48869392417111,"sku":"9783662633120","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662633120.jpg?v=1722292530"},{"product_id":"analysis-ii-9788195196128","title":"Analysis II","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.\u003cbr\u003e\u003cbr\u003eThe course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.\u003cbr\u003e\u003cbr\u003eThe fourth edition incorporates a large number of additional corrections reported since the release of the third edition, as well as some additional new exercises.","brand":"Hindustan Book Agency","offers":[{"title":"Default Title","offer_id":48869477482839,"sku":"9788195196128","price":44.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788195196128.jpg?v=1722292961"},{"product_id":"analysis-i-9788195196197","title":"Analysis I","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is part one of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.\u003cbr\u003e\u003cbr\u003eThe course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.\u003cbr\u003e\u003cbr\u003eThe fourth edition incorporates a large number of additional corrections reported since the release of the third edition, as well as some additional new exercises.","brand":"Hindustan Book Agency","offers":[{"title":"Default Title","offer_id":48869477679447,"sku":"9788195196197","price":49.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788195196197.jpg?v=1722292962"},{"product_id":"principles-of-mathematical-analysis-9780070856134","title":"Principles of Mathematical Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1: The Real and Complex Number Systems\u003cbr\u003eIntroduction\u003cbr\u003eOrdered Sets\u003cbr\u003eFields\u003cbr\u003eThe Real Field\u003cbr\u003eThe Extended Real Number System\u003cbr\u003eThe Complex Field\u003cbr\u003eEuclidean Spaces\u003cbr\u003eAppendix\u003cbr\u003eExercises\u003cbr\u003eChapter 2: Basic Topology\u003cbr\u003eFinite, Countable, and Uncountable Sets\u003cbr\u003eMetric Spaces\u003cbr\u003eCompact Sets\u003cbr\u003ePerfect Sets\u003cbr\u003eConnected Sets\u003cbr\u003eExercises\u003cbr\u003eChapter 3: Numerical Sequences and Series\u003cbr\u003eConvergent Sequences\u003cbr\u003eSubsequences\u003cbr\u003eCauchy Sequences\u003cbr\u003eUpper and Lower Limits\u003cbr\u003eSome Special Sequences\u003cbr\u003eSeries\u003cbr\u003eSeries of Nonnegative Terms\u003cbr\u003eThe Number e\u003cbr\u003eThe Root and Ratio Tests\u003cbr\u003ePower Series\u003cbr\u003eSummation by Parts\u003cbr\u003eAbsolute Convergence\u003cbr\u003eAddition and Multiplication of Series\u003cbr\u003eRearrangements\u003cbr\u003eExercises\u003cbr\u003eChapter 4: Continuity\u003cbr\u003eLimits of Functions\u003cbr\u003eContinuous Functions\u003cbr\u003eContinuity and Compactness\u003cbr\u003eContinuity and Connectedness\u003cbr\u003eDiscontinuities\u003cbr\u003eMonotonic Functions\u003cbr\u003eInfinite Limits and Limits at Infinity\u003cbr\u003eExercises\u003cbr\u003eChapter 5: Differentiation\u003cbr\u003eThe Derivative of a Real Function\u003cbr\u003eMean Value Theorems\u003cbr\u003eThe Continuity of Derivatives\u003cbr\u003eL'Hospital's Rule\u003cbr\u003eDerivatives of Higher-Order\u003cbr\u003eTaylor's Theorem\u003cbr\u003eDifferentiation of Vector-valued Functions\u003cbr\u003eExercises\u003cbr\u003eChapter 6: The Riemann-Stieltjes Integral\u003cbr\u003eDefinition and Existence of the Integral\u003cbr\u003eProperties of the Integral\u003cbr\u003eIntegration and Differentiation\u003cbr\u003eIntegration of Vector-valued Functions\u003cbr\u003eRectifiable Curves\u003cbr\u003eExercises\u003cbr\u003eChapter 7: Sequences and Series of Functions\u003cbr\u003eDiscussion of Main Problem\u003cbr\u003eUniform Convergence\u003cbr\u003eUniform Convergence and Continuity\u003cbr\u003eUniform Convergence and Integration\u003cbr\u003eUniform Convergence and Differentiation\u003cbr\u003eEquicontinuous Families of Functions\u003cbr\u003eThe Stone-Weierstrass Theorem\u003cbr\u003eExercises\u003cbr\u003eChapter 8: Some Special Functions\u003cbr\u003ePower Series\u003cbr\u003eThe Exponential and Logarithmic Functions\u003cbr\u003eThe Trigonometric Functions\u003cbr\u003eThe Algebraic Completeness of the Complex Field\u003cbr\u003eFourier Series\u003cbr\u003eThe Gamma Function\u003cbr\u003eExercises\u003cbr\u003eChapter 9: Functions of Several Variables\u003cbr\u003eLinear Transformations\u003cbr\u003eDifferentiation\u003cbr\u003eThe Contraction Principle\u003cbr\u003eThe Inverse Function Theorem\u003cbr\u003eThe Implicit Function Theorem\u003cbr\u003eThe Rank Theorem\u003cbr\u003eDeterminants\u003cbr\u003eDerivatives of Higher Order\u003cbr\u003eDifferentiation of Integrals\u003cbr\u003eExercises\u003cbr\u003eChapter 10: Integration of Differential Forms\u003cbr\u003eIntegration\u003cbr\u003ePrimitive Mappings\u003cbr\u003ePartitions of Unity\u003cbr\u003eChange of Variables\u003cbr\u003eDifferential Forms\u003cbr\u003eSimplexes and Chains\u003cbr\u003eStokes' Theorem\u003cbr\u003eClosed Forms and Exact Forms\u003cbr\u003eVector Analysis\u003cbr\u003eExercises\u003cbr\u003eChapter 11: The Lebesgue Theory\u003cbr\u003eSet Functions\u003cbr\u003eConstruction of the Lebesgue Measure\u003cbr\u003eMeasure Spaces\u003cbr\u003eMeasurable Functions\u003cbr\u003eSimple Functions\u003cbr\u003eIntegration\u003cbr\u003eComparison with the Riemann Integral\u003cbr\u003eIntegration of Complex Functions\u003cbr\u003eFunctions of Class L2\u003cbr\u003eExercises\u003cbr\u003eBibliography\u003cbr\u003eList of Special Symbols\u003cbr\u003eIndex\u003cbr\u003e","brand":"McGraw-Hill Education - Europe","offers":[{"title":"Default Title","offer_id":48883782222167,"sku":"9780070856134","price":53.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780070856134.jpg?v=1722529021"},{"product_id":"applied-calculus-for-business-economics-and-the-social-and-life-sciences-expanded-edition-9780071317849","title":"Applied Calculus for Business Economics and the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cem\u003eApplied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition \u003c\/em\u003eprovides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author''s applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1: Functions, Graphs, and Limits1.1 Functions1.2 The Graph of a Function1.3 Linear Functions1.4 Functional Models1.5 Limits1.6 One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1 The Derivative2.2 Techniques of Differentiation2.3 Product and Quotient Rules; Higher-Order Derivatives2.4 The Chain Rule2.5 Marginal Analysis and Approximations Using Increments2.6 Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration with Applications5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Area Between Curves and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper IntegralsChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsChapter 8: Trigonometric Functions8.1 Angle Measurement; Trigonometric Functions8.2 Derivatives of Trigonometric Functions8.3 Integrals of Trigonometric FunctionsChapter 9: Differential Equations9.1 Introduction to Differential Equations9.2 First-Order Linear Differential Equations9.3 Additional Applications of Differential Equations9.4 Approximate Solutions of Differential Equations9.5 Difference Equations; The Cobweb ModelChapter 10: Probability and Calculus10.1 Continuous Probability Distributions10.2 Expected Value and Variance10.3 Normal DistributionsChapter 11: Infinite Series and Taylor Series Approximations11.1 Infinite Series; Geometric Series11.2 Tests for Convergence11.3 Functions as Power Series; Taylor SeriesAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation","brand":"McGraw-Hill Education - Europe","offers":[{"title":"Default Title","offer_id":48883782680919,"sku":"9780071317849","price":56.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780071317849.jpg?v=1722529024"},{"product_id":"thomas-calculus-si-units-mylab-mathematics-with-pearson-etext-9781292459707","title":"Thomas Calculus SI Units  MyLab Mathematics with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Pearson Education","offers":[{"title":"Default Title","offer_id":48885386740055,"sku":"9781292459707","price":78.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292459707.jpg?v=1722536178"},{"product_id":"physics-for-scientists-and-engineers-9781337553278","title":"Physics for Scientists and Engineers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART I: MECHANICS. 1. Physics and Measurement. 2. Motion in One Dimension. 3. Vectors. 4. Motion in Two Dimensions. 5. The Laws of Motion. 6. Circular Motion and Other Applications of Newton's Laws. 7. Energy of a System. 8. Conservation of Energy. 9. Linear Momentum and Collisions. 10. Rotation of a Rigid Object About a Fixed Axis. 11. Angular Momentum. 12. Static Equilibrium and Elasticity. 13. Universal Gravitation. 14. Fluid Mechanics. PART II: OSCILLATIONS AND MECHANICAL WAVES. 15. Oscillatory Motion. 16. Wave Motion. 17. Superposition and Standing Waves. PART III: THERMODYNAMICS. 18. Temperature. 19. The First Law of Thermodynamics. 20. The Kinetic Theory of Gases. 21. Heat Engines, Entropy, and the Second Law of Thermodynamics. Part IV: ELECTRICITY AND MAGNETISM. 22. Electric Fields. 23. Continuous Charge Distributions and Gauss's Law. 24. Electric Potential. 25. Capacitance and Dielectrics. 26. Current and Resistance. 27. Direct-Current Circuits. 28. Magnetic Fields. 29. Sources of the Magnetic Field. 30. Faraday's Law. 31. Inductance. 32. Alternating-Current Circuits. 33. Electromagnetic Waves. PART V: LIGHT AND OPTICS. 34. The Nature of Light and the Principles of Ray Optics 35. Image Formation. 36. Wave Optics. 37. Diffraction Patterns and Polarization. PART VI: MODERN PHYSICS. 38. Relativity. APPENDICES. A. Tables. B. Mathematics Review. C. Periodic Table of the Elements. D. SI Units. Answers to Quick Quizzes and Odd-Numbered Problems. Index.","brand":"Cengage Learning, Inc","offers":[{"title":"Default Title","offer_id":48885433368919,"sku":"9781337553278","price":74.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781337553278.jpg?v=1722536365"}],"url":"https:\/\/bookcurl.com\/collections\/calculus-and-mathematical-analysis.oembed?page=20","provider":"Book Curl","version":"1.0","type":"link"}