{"title":"Integral calculus and equations Books","description":"","products":[{"product_id":"fractal-geometry-complex-dimensions-and-zeta-functions-9781461421757","title":"Fractal Geometry Complex Dimensions and Zeta","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This interesting volume gives a thorough introduction to an active field of research and will be very valuable to graduate students and researchers alike.” (C. Baxa, Monatshefte für Mathematik, Vol. 180, 2016)\u003c\/p\u003e\u003cp\u003e“In this research monograph the authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner the results … are completely proved. I appreciate that the book is useful for mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying the fractals and dimension theory.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, April, 2013)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e“The authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner, the results (including some fundamental ones) are completely proved. … the book will be useful to mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying fractals and dimension theory.” (Nicolae-Adrian Secelean, Zentralblatt MATH, Vol. 1261, 2013)\u003c\/p\u003e\u003cp\u003e\"In this book the author encompasses a broad range of topics that connect many areas of mathematics, including fractal geometry, number theory, spectral geometry, dynamical systems, complex analysis, distribution theory and mathematical physics. The book is self containing, the material organized in chapters preceding by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actual and has many applications.\" -- Nicolae-Adrian Secelean for Zentralblatt MATH\u003c\/p\u003e\u003cp\u003e\"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style.\" -- Mathematical Reviews (Review of previous book by authors)\u003c\/p\u003e\u003cp\u003e\"It is the reviewera (TM)s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced.\" -- Bulletin of the London Mathematical Society (Review of previous book by authors)\u003c\/p\u003e\u003cp\u003e\"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.\" -- Simulation News Europe (Review of previous book by authors)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- Overview.- Introduction.- 1. Complex Dimensions of Ordinary Fractal Strings.- 2. Complex Dimensions of Self-Similar Fractal Strings.- 3. Complex Dimensions of Nonlattice Self-Similar Strings.- 4. Generalized Fractal Strings Viewed as Measures.- 5. Explicit Formulas for Generalized Fractal Strings.- 6. The Geometry and the Spectrum of Fractal Strings.- 7. Periodic Orbits of Self-Similar Flows.- 8. Fractal Tube Formulas.- 9. Riemann Hypothesis and Inverse Spectral Problems.- 10. Generalized Cantor Strings and their Oscillations.- 11. Critical Zero of Zeta Functions.- 12 Fractality and Complex Dimensions.- 13. Recent Results and Perspectives.- Appendix A. Zeta Functions in Number Theory.- Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics.- Appendix C. An Application of Nevanlinna Theory.- Bibliography.- Author Index.- Subject Index.- Index of Symbols.- Conventions.- Acknowledgements.\u003c\/p\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739348971863,"sku":"9781461421757","price":107.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461421757.jpg?v=1720051981"},{"product_id":"differentiability-in-banach-spaces-differential-forms-and-applications-9783030778330","title":"Differentiability in Banach Spaces, Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“A specific feature of the book is the abundance of examples from mechanics, physics, calculus of variations, illustrating the abstract concepts introduced in the main text. … There are a lot of exercises spread through the book, some elementary, while others are more advanced. The book can be used as supplementary material for undergraduate or graduate level courses, as well as by the students in physics interested in a mathematical treatment of some important problems in their domain.” (Stefan Cobzaş, zbMATH 1479.46001, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Chapter 1. Differentiation in R^n.- Chapter 2. Linear Operators in Banach Spaces.- Chapter 3. Differentiation in Banach Spaces.- Chapter 4. Vector Fields.- Chapter 5. Vectors Integration, Potential Theory.- Chapter 6. Differential Forms, Stoke’s Theorem.- Chapter 7. Applications to the Stoke’s Theorem.- Appendix A. Basics of Analysis.- Appendix B. Differentiable Manifolds, Lie Groups.- Appendix C. Tensor Algebra.- Bibliography.- Index.\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743049363799,"sku":"9783030778330","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"measure-theory-probability-and-stochastic-processes-9783031142048","title":"Measure Theory, Probability, and Stochastic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.\u003c\/p\u003eArranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eMeasure Theory, Probability, and Stochastic Processes\u003c\/i\u003e is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author’s more advanced textbook in the same series (GTM 274).\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I. Measure Theory.- Chapter 1. Measurable Spaces.- Chapter 2. Integration of Measurable Functions.- Chapter 3. Construction of Measures.- Chapter 4. Lp Spaces.- Chapter 5. Product Measure.- Chapter 6. Signed Measures.- Chapter 7. Change of Variables.- Part II. Probability Theory.- Chapter 8. Foundations of Probability Theory.- Chapter 9. Independence.- Chapter 10. Convergence of Random Variables.- Chapter 11. Conditioning.- Part III. Stochastic Processes.- Chapter 12. Theory of Martingales.- Chapter 13. Markov Chains.- Chapter 14. Brownian Motion.  ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743072629079,"sku":"9783031142048","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"the-big-book-of-real-analysis-from-numbers-to-measures-9783031308314","title":"The Big Book of Real Analysis: From Numbers to","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus.\u003c\/p\u003e  \u003cp\u003eBeginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the study of measures and how one can construct the Lebesgue integral as an extension of the Riemann integral.\u003c\/p\u003e  \u003cp\u003eThis textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- 1. Logic and Sets.- 2. Integers.- 3. Construction of the Real Numbers.- 4. The Real Numbers.- 5. Real Sequences.- 6. Some Applications of Real Sequences.- 7. Real Series.- 8. Additional Topics in Real Series.- 9. Functions and Limits.- 10. Continuity.- 11. Function Sequences and Series.- 12. Power Series.- 13. Differentiation.- 14. Some Applications of Differentiation.- 15. Riemann and Darboux Integration.- 16. The Fundamental Theorem of Calculus.- 17. Taylor and MacLaurin Series.- 18. Introduction to Measure Theory.- 19. Lebesgue Integration.- 20. Double Integrals.- Solutions to the Exercises.- Bibliography.- Index. \u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743080165719,"sku":"9783031308314","price":80.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031308314.jpg?v=1720064022"},{"product_id":"calculus-ii-practice-problems-methods-and-solutions-9783031453526","title":"Calculus II: Practice Problems, Methods, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis study guide is designed for students taking a Calculus II course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes applications of integration, sequences and series and their applications, polar coordinate systems, and complex numbers. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students’ problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eChapter 1: Problems: Applications of integration.- Chapter 2: Solutions of Problems: Applications of integration.- Chapter 3: Problems: Sequences and series and their applications.- Chapter 4: Solutions of Problems: Sequences and series and their applications.- Chapter 5: Problems: Polar coordinate system.- Chapter 6: Solutions of Problems: Polar coordinate system.- Chapter 7: Problems: Complex numbers.- Chapter 8: Solutions of Problems: Complex numbers.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743086686551,"sku":"9783031453526","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031453526.jpg?v=1722247509"},{"product_id":"multivariable-calculus-with-matlab-r-with-applications-to-geometry-and-physics-9783319650692","title":"Multivariable Calculus with MATLAB®: With","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. \u003c\/p\u003e  \u003cp\u003eMATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book is addressed to students as well as to instructors of calculus. It helps to understand multivariable analysis utilysing visualization of such geometric structures like domains, curves and surfaces. It also develops the skill of students to use a powerful software for solving modern problems.” (Ivan Podvigin, zbMATH 1400.26001, 2019)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Vectors and Graphics.- 3. Geometry of Curves.- 4. Kinematics.- 5. Directional Derivatives.- 6. Geometry of Surfaces.- 7. Optimization in Several Variables.- 8. Multiple Integrals.- 9. Multidimensional Calculus.- 10. Physical Applications of Vector Calculus.- 11. MATLAB Tips.- Sample Solutions.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743100940631,"sku":"9783319650692","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319650692.jpg?v=1720064115"},{"product_id":"real-analysis-and-applications-9783319786308","title":"Real Analysis and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. \u003cbr\u003eWith its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 01- Real Numbers.- Chapter 02- Metric Spaces.- Chapter 03- Real Sequences and Series.- Chapter 04- Real Function Limits.- Chapter 05- Continuous Functions.- Chapter 06- Derivatives.- Chapter 07- The Riemann Integral.- Chapter 08- Differential Analysis in Rn.- Chapter 09- Integration in Rn.- Chapter 10- Topics on Vector Calculus and Vector Analysis.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743106675031,"sku":"9783319786308","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319786308.jpg?v=1720064138"},{"product_id":"theories-of-integration-the-integrals-of-riemann-lebesgue-henstock-kurzweil-and-mcshane-9789814368995","title":"Theories Of Integration: The Integrals Of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction: Areas; Exercises; Riemann Integral: Riemann's Definition; Basic Properties; Cauchy Criterion; Darboux's Definition; Fundamental Theorem of Calculus; Characterizations of Integrability; Improper Integrals; Exercises; Convergence Theorems and the Lebesgue Integral: Lebesgue's Descriptive Definition of the Integral; Measure; Lebesgue Measure in ℝn; Measurable Functions; Lebesgue Integral; Riemann and Lebesgue Integrals; Mikusinski's Characterization of the Lebesgue Integral; Fubini's Theorem; The Space of Lebesgue Integrable Functions; Exercises; Fundamental Theorem of Calculus and the Henstock - Kurzweil Integral: Denjoy and Perron Integrals; A General Fundamental Theorem of Calculus; Basic Properties; Unbounded Intervals; Henstock's Lemma; Absolute Integrability; Convergence Theorems; Henstock - Kurzweil and Lebesgue Integrals; Differentiating Indefinite Integrals; Characterizations of Indefinite Integrals; The Space of Henstock - Kurzweil Integrable Functions; Henstock - Kurzweil Integrals on ℝn; Exercises; Absolute Integrability and the McShane Integral: Defintions; Basic Properties; Absolute Integrability; Convergence Theorems; The McShane Integral as a Set Function; The Space of McShane Integrable Functions; McShane, Henstock - Kurzweil and Lebesgue Integrals; McShane Integrals on ℝn; Fubini and Tonelli Theorems; McShane, Henstock - Kurzweil and Lebesgue Integrals in ℝn; Exercises.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743298826583,"sku":"9789814368995","price":66.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814368995.jpg?v=1720064984"},{"product_id":"probability-an-introduction-through-theory-and-exercises-9783031384912","title":"Probability: An Introduction Through Theory and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.\u003c\/p\u003e  \u003cp\u003eThe book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.\u003c\/p\u003e  \u003cp\u003eBased on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084758884695,"sku":"9783031384912","price":46.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031384912.jpg?v=1725553247"},{"product_id":"vector-integration-48-pure-and-applied-mathematics-a-wiley-series-of-texts-monographs-and-tracts-9780471377382","title":"Vector Integration 48 Pure and Applied","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...an important tool...gives the newest results in this field...shows an important application of vector integration...\" (Bulletin of the Belgian Mathematical Society, Vol 11(1), 2004)\u003cbr\u003e \u003cbr\u003e \"...it can be expected that...just like the author's 1967 volume, this book will stimulate further research on vector stochastic integration and can serve as a graduate-level reference work.\" (Mathematical Reviews Issue 2001h)\u003cbr\u003e \u003cbr\u003e \"Dense, detailed, comprehensive introduction. Contains...material only found before in journals...\" (American Mathematical Monthly, March 2002)\u003cbr\u003e \u003cbr\u003e \"...a highly technical book.\" (The Mathematical Gazette, March 2002)\u003cbr\u003e \u003cbr\u003e \"The author of this important and interesting book is a well-known specialist on vector measures.\" (Zentralblatt Math, Vol.974, No. 24 2001)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eVector Integration.\u003cbr\u003e \u003cbr\u003e The Stochastic Integral.\u003cbr\u003e \u003cbr\u003e Martingales.\u003cbr\u003e \u003cbr\u003e Processes with Finite Variation.\u003cbr\u003e \u003cbr\u003e Processes with Finite Semivariation.\u003cbr\u003e \u003cbr\u003e The Itô Formula.\u003cbr\u003e \u003cbr\u003e Stochastic Integration in the Plane.\u003cbr\u003e \u003cbr\u003e Two-Parameter Martingales.\u003cbr\u003e \u003cbr\u003e Two-Parameter Processes with Finite Variation.\u003cbr\u003e \u003cbr\u003e Two-Parameter Processes with Finite Semivariation.\u003cbr\u003e \u003cbr\u003e References.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402577715543,"sku":"9780471377382","price":170.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471377382.jpg?v=1730480820"},{"product_id":"ergodic-theory-with-a-view-towards-number-theory-graduate-texts-in-mathematics-259-9780857290205","title":"Ergodic Theory With a View Towards Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMotivation.- Ergodicity, Recurrence and Mixing.- Continued Fractions.- Invariant Measures for Continuous Maps.- Conditional Measures and Algebras.- Factors and Joinings.- Furstenberg's Proof of Szemeredi's Theorem.- Actions of Locally Compact Groups.- Geodesic Flow on Quotients of the Hyperbolic Plane.- Nilrotation.- More Dynamics on Quotients of the Hyperbolic Plane.- Appendix A: Measure Theory.- Appendix B: Functional Analysis.- Appendix C: Topological Groups\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The book is an introduction to ergodic theory and dynamical systems. … The book is intended for graduate students and researchers with some background in measure theory and functional analysis. Definitely, it is a book of great interest for researchers in ergodic theory, homogeneous dynamics or number theory.” (Antonio Díaz-Cano Ocaña, The European Mathematical Society, January, 2014)\u003c\/p\u003e\u003cp\u003e“A book with a wider perspective on ergodic theory, and yet with a focus on the interaction with number theory, remained a glaring need in the overall context of the development of the subject. … The book under review goes a long way in fulfilling this need. … it covers a good deal of conventional ground in ergodic theory … . a very welcome addition and would no doubt inspire interest in the area among researchers as well as students, and cater to it successfully.” (S. G. Dani, Ergodic Theory and Dynamical Systems, Vol. 32 (3), June, 2012)\u003c\/p\u003e\u003cp\u003e“The book under review is an introductory textbook on ergodic theory, written with applications to number theory in mind. … it aims both to provide the reader with a solid comprehensive background in the main results of ergodic theory, and of reaching nontrivial applications to number theory. … The book should also be very appealing to more advanced readers already conducting research in representation theory or number theory, who are interested in understanding the basis of the recent interaction with ergodic theory.” (Barak Weiss, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 114, 2012)\u003c\/p\u003e\u003cp\u003e“This introductory book, which goes beyond the standard texts and allows the reader to get a glimpse of modern developments, is a timely and welcome addition to the existing and ever-growing ergodic literature. … This book is highly recommended to graduate students and indeed to anyone who is interested in acquiring a better understanding of contemporary developments in mathematics.” (Vitaly Bergelson, Mathematical Reviews, Issue 2012 d)\u003c\/p\u003e\u003cp\u003e“The book contains a presentation of the ergodic theory field, focusing mainly on results applicable to number theory. … of interest for researchers, specialists, professors and students that work within some other areas than precisely the ergodic theory. … ‘Ergodic Theory. With a view toward number theory’ is now an indispensable reference in the domain and offers important instruments of research for other theoretical fields.” (Adrian Atanasiu, Zentralblatt MATH, Vol. 1206, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eMotivation.- Ergodicity, Recurrence and Mixing.- Continued Fractions.- Invariant Measures for Continuous Maps.- Conditional Measures and Algebras.- Factors and Joinings.- Furstenberg’s Proof of Szemeredi’s Theorem.- Actions of Locally Compact Groups.- Geodesic Flow on Quotients of the Hyperbolic Plane.- Nilrotation.- More Dynamics on Quotients of the Hyperbolic Plane.- Appendix A: Measure Theory.- Appendix B: Functional Analysis.- Appendix C: Topological Groups","brand":"Springer London Ltd","offers":[{"title":"Default Title","offer_id":49406291542359,"sku":"9780857290205","price":43.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780857290205.jpg?v=1730495260"},{"product_id":"recent-trends-in-naval-engineering-research-9783030641504","title":"Recent Trends in Naval Engineering Research","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis multidisciplinary volume is the second in the STEAM-H series to feature invited contributions on mathematical applications in naval engineering. Seeking a more holistic approach that transcends current scientific boundaries, leading experts present interdisciplinary instruments and models on a broad range of topics. Each chapter places special emphasis on important methods, research directions, and applications of analysis within the field. \u003c\/p\u003e\u003cp\u003eFundamental scientific and mathematical concepts are applied to topics such as microlattice materials in structural dynamics, acoustic transmission in low Mach number liquid flow, differential cavity ventilation on a symmetric airfoil, Kalman smoother, metallic foam metamaterials for vibration damping and isolation, seal whiskers as a bio-inspired model for the reduction of vortex-induced vibrations, multidimensional integral for multivariate weighted generalized Gaussian distributions, minimum uniform search track placement for rectangular regions, antennas in the maritime environment, the destabilizing impact of non-performers in multi-agent groups, inertial navigation accuracy with bias modeling.\u003c\/p\u003e\u003cp\u003eCarefully peer-reviewed and pedagogically presented for a broad readership, this volume is perfect to graduate and postdoctoral students interested in interdisciplinary research. Researchers in applied mathematics and sciences will find this book an important resource on the latest developments in naval engineering. In keeping with the ideals of the STEAM-H series, this volume will certainly inspire interdisciplinary understanding and collaboration.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroductory Chapter: Mathematical Sciences and Naval Engineering Research.- Microlattice Materials and their potential applications in structural dynamics and acoustics.- Alternative Approach to Cagniard Method for Transient Ocean Acoustic Modeling.- Acoustic transmission in a low Mach number liquid flow.- Lift Production using Differential Cavity Ventilation.- An Exact Solution for a Kalman Smoother.- Metallic Foam Metamaterials for Vibration Damping and Isolation.- The other Navy Seals: Seal Whiskers as a Bio-Inspired Model for the Resolution of Vortex Induced Vibrations.- A series of multidimensional integral identities with applications to multivariate weighted generalized Gaussian Distributions.- Minimum Uniform Track Placement for Rectangular Regions.- Antenna Behavior in the Maritime Environment.- The Destabilizing impact of Non-Performers in Multi-Agent Groups.- Improving Inertial Navigation Accuracy with Bias Modeling.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415627047255,"sku":"9783030641504","price":87.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030641504.jpg?v=1730527565"},{"product_id":"perspectives-in-dynamical-systems-iii-control-and-stability-dsta-lodz-poland-december-2-5-2019-9783030773137","title":"Perspectives in Dynamical Systems III: Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems.\u003cbr\u003eThe broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eOn the spinning motion of a disc under the influence a gyrostatic moment (Gamiel).- Suppression of impact oscillations in a railway current collection system with an additional oscillatory system (Nishiyama).- On Qualitative Analysis of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array: Bifurcations and Transition to Chaos (Martsenyuk).- Response sensitivity of damper-connected adjacent structural systems subjected to fully non-stationary random excitations (Genovese).- Analysis of switching strategies for the optimization of periodic chemical reactions with controlled flow-rate (Zuyev).- Quaternion based free-floating space manipulator dynamics modeling using the dynamically equivalent manipulator approach (Jarzębowska).- Slosh analysis on a full car model with SDRE control and hydraulic damper (Balthazar).- A comparison of the common types of nonlinear energy sinks (Saeed).- Stability of three wheeled narrow vehicle (Weigel-Milleret).- Testing and analysis of vibrations of a tension transmission with a thermally sealed belt (Szymański).- Modeling and experimental tests on motion resistance of double-flange rollers of rubber track systems due to sliding friction between the rollers and guide lugs of rubber tracks (Chołodowski).- Structural dynamic response of the coupling between transmission lines and tower under random excitation (Machado).- Experimental assessment of the test station support structure rigidity by the vibration diagnostics method (Šmeringaiová).- Experimental dynamical analysis of a mechatronic analogy of the human circulatory system (Olejnik).- Robust design of inhibitory neuronal networks displaying rhythmic activity (Taylor).- Nonlinear dynamics of the industrial city's atmospheric ventilation: New differential equations model and chaos (Buyadzhi).- Biomechanical analysis of different foot morphology during standing on a dynamic support surface (Shu).- Comparison of various fractional order controllers on a poorly damped system (Birs).- Asymptotic analysis of submerged spring pendulum motion in liquid (Amer).- Parametric identification of non linear structures using Particle Swarm Optimization based on power flow balance criteria (Rajan).- Vibration and buckling of laminated plates of complex form under in-plane uniform and non-uniform loading (Linnik).- Dynamical systems and stability in fractional solid mechanics (Beda).- Stability of coupled systems of stochastic Cohen-Grossberg neural networks with time delays, impulses and Markovian switching (Tojtovska).- Stability of steady states with regular or chaotic behaviour in time (Mikhlin).- Modelling of torsional vibrations in a motorcycle steering system (Dębowski).- Free vibration frequencies of simply supported bars with variable cross section (Szlachetka).- On dynamics of a rigid block on visco-elastic foundation (Garziera).","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415637860695,"sku":"9783030773137","price":119.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030773137.jpg?v=1730527607"},{"product_id":"the-krasnoselskii-mann-iterative-method-recent-progress-and-applications-9783030916534","title":"The Krasnosel'skiĭ-Mann Iterative Method: Recent","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis brief explores the Krasnosel'skiĭ-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.  \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Notation and Mathematical Foundations.-3. The Krasnoselskii-Mann Iteration.- 4. Relations of the Krasnosel'skii-Mann Iteration and the Operator Splitting Methods.- 5. The Inertial Krasnoselskii-Mann Iteration.- 6. The Multi-step Inertial Krasnoselskii-Mann Iteration.- 7. Relaxation Parameters of the Krasnoselskii-Mann Iteration.- 8. Two Applications.\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415659094359,"sku":"9783030916534","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030916534.jpg?v=1730527686"},{"product_id":"linear-systems-9783031212390","title":"Linear Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis.\u003cbr\u003eThe book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar’s model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittaker’s sampling theorem for band-limited functions, and Shannon’s wavelet.\u003cbr\u003eBased on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- 1. Linear Systems and Their Description. - 2. Solving Linear Systems by Matrix Theory. - 3. Eigenvalues and Block Decompositions of Matrices. - 4. Laplace Transforms. - 5. Transfer Functions, Frequency Response, Realization and Stability. - 6. Algebraic Characterizations of Stability. - 7. Stability and Transfer Functions via Linear Algebra. - 8. Discrete Time Systems. - 9. Random Linear Systems and Green’s Functions. - 10. Hilbert Spaces. - 11. Wireless Transmission and Wavelets. - 12. Solutions to Selected Exercises.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415698219351,"sku":"9783031212390","price":47.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031212390.jpg?v=1730527826"},{"product_id":"fractional-differential-equations-new-advancements-for-generalized-fractional-derivatives-9783031348761","title":"Fractional Differential Equations: New","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction.- Preliminary Background.- Hybrid Fractional Differential Equations.- Fractional Differential Equations with Retardation and Anticipation.- Impulsive Fractional Differential Equations with Retardation and Anticipation.- Coupled Systems for Fractional Differential Equations.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415711555927,"sku":"9783031348761","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031348761.jpg?v=1730527871"},{"product_id":"inverse-acoustic-and-electromagnetic-scattering-theory-9783030303532","title":"Inverse Acoustic and Electromagnetic Scattering","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe inverse scattering problem is central to many areas of science and technology such as radar, sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. \u003c\/p\u003e\u003cp\u003eIn this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- Ill-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- AcousticWaves in an Inhomogeneous Medium.- ElectromagneticWaves in an Inhomogeneous Medium.- Transmission Eigenvalues.- The Inverse Medium Problem.\u003cbr\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":50470469042519,"sku":"9783030303532","price":104.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030303532.jpg?v=1744898421"},{"product_id":"singular-integral-operators-quantitative-flatness-and-boundary-problems-9783031082337","title":"Singular Integral Operators, Quantitative","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Geometric Measure Theory.- Calderon-Zygmund Theory for Boundary Layers in UR Domains.- Boundedness and Invertibility of Layer Potential Operators.- Controlling the BMO Semi-Norm of the Unit Normal.- Boundary Value Problems in Muckenhoupt Weighted Spaces.- Singular Integrals and Boundary Problems in Morrey and Block Spaces.- Singular Integrals and Boundary Problems in Weighted Banach Function Spaces.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":50470475039063,"sku":"9783031082337","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031082337.jpg?v=1744898435"},{"product_id":"theory-and-applications-of-special-functions-for-scientists-and-engineers-9789813363335","title":"Theory and Applications of Special Functions for","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world phenomena in mathematical physics, engineering and other applied sciences. The audience benefits of new and original information and references in the areas of the special functions applied to model the complex problems with the power-law behaviors.\u003cbr\u003eThe results are important and interesting for scientists and engineers to represent the complex phenomena arising in applied sciences therefore graduate students and researchers in mathematics, physics and engineering might find this book appealing.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eChapter 1 Preliminaries.- Chapter 2 Wright Function and Integral Transforms via Dunkl Transform.- Chapter 3 Mittag-Leffler, Supertrigonometric and Superhyperbolic Functions.- Chapter 4 Wiman, Supertrigonometric and Superhyperbolic Functions.- Chapter 5 Prabhakar, Supertrigonometric and Superhyperbolic Functions.- Chapter 6 Other Special Functions Related to Mittag-Leffler Function.- Chapter 7 Kohlrausch-Williams-Watts Function and Related Topics Bibliography.\u003c\/p\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":50473268052311,"sku":"9789813363335","price":95.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789813363335.jpg?v=1744905920"},{"product_id":"inverse-scattering-theory-and-transmission-eigenvalues-9781611977417","title":"Inverse Scattering Theory and Transmission","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eInverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. \u003cbr\u003e\u003cbr\u003eIn the first edition of \u003ci\u003eInverse Scattering Theory and Transmission Eigenvalues\u003c\/i\u003e, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. \u003cbr\u003e\u003cbr\u003eIn particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles.\u003cbr\u003e\u003cbr\u003eThis book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.","brand":"Society for Industrial \u0026 Applied Mathematics,U.S.","offers":[{"title":"Default Title","offer_id":50578265211223,"sku":"9781611977417","price":64.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781611977417.jpg?v=1746098585"},{"product_id":"real-mathematical-analysis-9783319177700","title":"Real Mathematical Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eBased on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.\u003cbr\u003e\u003cbr\u003eNew to the second edition of \u003ci\u003eReal Mathematical Analysis\u003c\/i\u003e is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line\/one-picture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to \u003ci\u003esee\u003c\/i\u003e an integral result from measure theory. The presentation includes Vitali’s Covering Lemma, density points — which are rarely treated in books at this level — and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book, in its second edition, provides the basic concepts of real analysis. ... I strongly recommend it to everyone who wishes to study real mathematical analysis.\" (Catalin Barbu, zbMATH 1329.26003, 2016)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eReal Numbers.- A Taste of Topology.- Functions of a Real Variable.- Function Spaces.- Multivariable Calculus.- Lebesgue Theory.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":50578842976599,"sku":"9783319177700","price":38.94,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319177700.jpg?v=1746101110"},{"product_id":"generalized-functions-theory-and-applications-9780817643430","title":"Generalized Functions Theory And Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- The Dirac Delta Function and Delta Sequences.- The Schwartz-Sobolev Theory of Distributions.- Additional Properties of Distributions.- Distributions Defined by Divergent Integrals.- Distributional Derivatives of Functions with Jump Discontinuities.- Tempered Distributions and the Fourier Transforms.- Direct Products and Convolutions of Distributions.- The Laplace Transform.- Applications to Ordinary Differential Equations.- Applications to Partial Differential Equations.- Applications to Boundary Value Problems.- Applications to Wave Propagation.- Interplay between Generalized Functions and the Theory of Moments.- Linear Systems.- Miscellaneous Topics.- References.- Index.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This book on generalized functions is suitable for physicists, engineers and applied mathematicians. The author presents the notion of generalized functions, their properties and their applications for solving ordinary differential equations and partial differential equations. ...\u003c\/p\u003e \u003cp\u003eThe author demonstrates through various examples that familiarity with generalized functions is very helpful for students in mathematics, physical sciences and technology. The proposed exercises are very good for better understanding of notions and properties presented in the chapters. The book contains new topics and important features.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—Mathematica\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"The advantage of this text is in carefully gathered examples explaining how to use corresponding properties.... Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology.\" \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—Zentralblatt \u003c\/strong\u003e\u003cstrong\u003e(Review of a previous edition)\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"The author has done an excellent job in presenting examples and in displaying the calculational techniques associated with distributions and the applications. Throughout the book there are a wealth of examples concerning the distributional topics and caluclations introduced and concering the applications, and the examples are presented in detail.\" \u003cstrong\u003e---Zentralblatt (Review of the 1st edition)\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"The collaboration of physicists or engineers and mathematics, which is more and more popular and necessary in modern investigations, requires…a common language. The book under review provides this language…. [It] is a well written book, most of the material is accessible to senior undergraduate and graduate students in mathematical, physical and engineering sciences…. [The] book will [also] be useful…for specialists in ODEs, PDEs, functional analysis, [and] physicists, engineers, and lecturers.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—Acta. Sci. Math. (Review of a previous edition)\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/p\u003e\"An exceptionally clear exposition... The exercises at the end of each chapter are well-chosen.\"  \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—The American Mathematical Monthly (Review of a previous edition)\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"This fully revised edition of well-received book expands the treatment of fundamental concepts and theoretical background material delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optical control problems in economics, and more.  It has many new topics and [features] driven by additional examples and exercises. . . It presents a wealth of applications that connot be found in any other single source.  the book will be important reading for graduate students in physics and engineering.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e--- Educational  Book Review\u003c\/strong\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface to the Third Edition * Preface to the Second Edition * Preface to the First Edition * Chapter 1. The Dirac Delta Function and Delta Sequences * 1.1 The Heaviside Function * 1.2 The Dirac Delta Function * 1.3 The Delta Sequences * 1.4 A Unit Dipole * 1.5 The Heaviside Sequences * Exercises * Chapter 2. The Schwartz-Sobolev Theory of Distributions * 2.1 Some Introductory Definitions * 2.2 Test Functions * 2.3 Linear Functionals and the Schwartz–Sobolev Theory of Distributions * 2.4 Examples * 2.5 Algebraic Operations on Distributions * 2.6 Analytic Operations on Distributions * 2.7 Examples * 2.8 The Support and Singular Support of a Distribution Exercises * Chapter 3. Additional Properties of Distributions * 3.1 Transformation Properties of the Delta Distributions * 3.2 Convergence of Distributions * 3.3 Delta Sequences with Parametric Dependence * 3.4 Fourier Series * 3.5 Examples * 3.6 The Delta Function as a Stieltjes Integral Exercises * Chapter 4. Distributions Defined by Divergent Integrals * 4.1 Introduction * 4.2 The Pseudofunction H(x)\/x n , n = 1, 2,3, * 4.3 Functions with Algebraic Singularity of Order m * 4.4 Examples * Exercises * Chapter 5. Distributional Derivatives of Functions with Jump Discontinuities * 5.1 Distributional Derivatives in R 1 * 5.2 Moving Surfaces of Discontinuity in R n , n 2 * 5.3 Surface Distributions * 5.4 Various Other Representations * 5.5 First-Order Distributional Derivatives * 5.6 Second Order Distributional Derivatives * 5.7 Higher-Order Distributional Derivatives * 5.8 The Two-Dimensional Case * 5.9 Examples * 5.10 The Function Pf ( l\/r ) and its Derivatives * Chapter 6. Tempered Distributions and the Fourier Transforms * 6.1 Preliminary Concepts * 6.2 Distributions of Slow Growth (Tempered Distributions) * 6.3 The Fourier Transform * 6.4 Examples * Exercises * Chapter 7. Direct Products and Convolutions of Distributions * 7.1 Definition of the Direct Product * 7.2 The Direct Product of Tempered Distributions * 7.3 The Fourier Transform of the Direct Product of Tempered Distributions * 7.4 The Convolution * 7.5 The Role of Convolution in the Regularization of the Distributions * 7.6 The Dual Spaces E and E' * 7.7 Examples * 7.8 The Fourier Transform of the Convolution * 7.9 Distributional Solutions of Integral Equations * Exercises * Chapter 8. The Laplace Transform * 8.1 A Brief Discussion of the Classical Results * 8.2 The Laplace Transform of the Distributions * 8.3 The Laplace Transform of the Distributional Derivatives and Vice Versa * 8.4 Examples * Exercises * Chapter 9. Applications to Ordinary Differential Equations * 9.1 Ordinary Differential Operators * 9.2 Homogeneous Differential Equations * 9.3 Inhomogeneous Differentational Equations: The Integral of a Distribution * 9.4 Examples * 9.5 Fundamental Solutions and Green's Functions * 9.6 Second Order Differential Equations with Constant Coefficients * 9.7 Eigenvalue Problems * 9.8 Second Order Differential Equations with Variable Coefficients * 9.9 Fourth Order Differential Equations * 9.10 Differential Equations of n th Order * 9.11 Ordinary Differential Equations with Singular Coefficients * Exercises * Chapter 10. Applications to Partial Differential Equations * 10.1 Introduction * 10.2 Classical and Generalized Solutions * 10.3 Fundamental Solutions * 10.4 The Cauchy–Riemann Operator * 10.5 The Transport Operator * 10.6 The Laplace Operator * 10.7 The Heat Operator * 10.8 The Schroedinger Operator * 10.9 The Helmholtz Operator * 10.10 The Wave Operator * 10.11 The Inhomogeneous Wave Equation * 10.12 The Klein–Gordon Operator * Exercises * Chapter 11. Applications to Boundary Value Problems * 11.1 Poisson's Equation * 11.2 Dumbbell-Shaped Bodies * 11.3 Uniform Axial Distributions * 11.4 Linear Axial Distributions * 11.5 Parabolic Axial Distributions * 11.6 The Four-Order Polynomial Distribution, n = 7; Spheroidal Cavities * 11.7 The Polarization Tensor for a Spheroid * 11.8 The Virtual Mass Tensor for a Spheroid * 11.9 The Electric and Magnetic Polarizability Tensors * 11.10 The Distributional Approach to Scattering Theory * 11.11 Stokes Flow * 11.12 Displacement-Type Boundary Value Problems in Elastostatics * 11.13 The Extension to Elastodynamics * 11.14 Distributions on Arbitrary Lines * 11.15 Distributions on Plane Curves * 11.16 Distributions on a Circular Disk * Chapter 12. Applications to Wave Propagation * 12.1 Introduction * 12.2 The Wave Equation * 12.3 First-Order Hyperbolic Systems * 12.4 Aerodynamic Sound Generation * 12.5 The Rankine–Hugoniot Conditions * 12.6 Wave Fronts That Carry Infinite Singularities * 12.7 Kinematics of Wave Fronts * 12.8 Derivation of the Transport Theorems for Wave Fronts * 12.9 Propagation of Wave Fronts Carrying Multilayer Densities * 12.10 Generalized Functions with Support on the Light Cone * 12.11 Examples * Chapter 13. Interplay Between Generalized Functions and the Theory of Moments * 13.1 The Theory of Moments * 13.2 Asymptotic Approximation of Integrals * 13.3 Applications to the Singular Perturbation Theory * 13.4 Applications to Number Theory * 13.5 Distributional Weight Functions for Orthogonal Polynomials * 13.6 Convolution Type Integral Equations Revisited * 13.7 Further Applications * Chapter 14. Linear Systems * 14.1 Operators * 14.2 The Step Response * 14.3 The Impulse Response * 14.4 The Response to an Arbitrary Input * 14.5 Generalized Functions as Impulse Response Functions * 14.6 The Transfer Function * 14.7 Discrete-Time Systems * 14.8 The Sampling Theorem * Chapter 15. Miscellaneous Topics * 15.1 Applications to Probability and Statistics * 15.2 Applications to Mathematical Economics * 15.3 Periodic Generalized Functions * 15.4 Microlocal Theory * References * Index\u003c\/p\u003e","brand":"Birkhäuser","offers":[{"title":"Default Title","offer_id":51018475209047,"sku":"9780817643430","price":80.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817643430.jpg?v=1750777030"},{"product_id":"lectures-on-convex-geometry-9783030501822","title":"Lectures on Convex Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a self-contained introduction to convex geometry in Euclidean space.  After covering the basic concepts and results, it develops Brunn–Minkowski  theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including  the isoperimetric inequality.  Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations.  Finally, an introduction to integral-geometric formulas in Euclidean space is provided.  The numerous exercises and the supplementary material at the end of each section form an essential part of the book.\u003c\/p\u003e  \u003cp\u003eConvexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry.\u003c\/p\u003e  \u003cp\u003ePaving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“‘Lectures on convex geometry’ is an excellent graduate book about convex geometry. … The book is very well-organized. … The presentation is clear, well-composed and illustrated. The problems at the end of each subchapter are carefully selected and revised. The whole text is readable, interesting and easy to learn from. … the book is excellent and it can serve the studies of the future generation students in convex geometry.” (Gergely Kiss, zbMATH 1487.52001, 2022)\u003cbr\u003e“The book is informative, very interesting, and mathematically accessible, and the authors have achieved the purpose that they outline above. As the title suggests, Lectures on convex geometry is well suited to be used as the prescribed textbook for graduate courses in convex geometry; this is because of its pedagogical style and the quality of the exercises. It will also be useful to students intending to pursue a research career in the area … .” (Daniel John Fresen, Mathematical Reviews, June, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Preliminaries and Notation.- 1. Convex Sets.- 2. Convex Functions.- 3. Brunn-Minkowski Theory.- 4. From Area Measures to Valuations.- 5. Integral Geometric Formulas.-6. Solutions of Selected Exercises.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":51021119652183,"sku":"9783030501822","price":39.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030501822.jpg?v=1750785223"},{"product_id":"probability-theory-a-comprehensive-course-9783030564018","title":"Probability Theory: A Comprehensive Course","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory.\u003cp\u003eProbability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms.  Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as:\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003elimit theorems for sums of random variables\u003c\/li\u003e\n\u003cli\u003emartingales\u003c\/li\u003e\n\u003cli\u003epercolation\u003c\/li\u003e\n\u003cli\u003eMarkov chains and electrical networks\u003c\/li\u003e\n\u003cli\u003econstruction of stochastic processes\u003c\/li\u003e\n\u003cli\u003ePoisson point process and infinite divisibility\u003c\/li\u003e\n\u003cli\u003elarge deviation principles and statistical physics\u003c\/li\u003e\n\u003cli\u003eBrownian motion\u003c\/li\u003e\n\u003cli\u003estochastic integrals and stochastic differential equations.\u003c\/li\u003e\n\u003c\/ul\u003e The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Basic Measure Theory.- 2 Independence.- 3 Generating Functions.- 4 The Integral.- 5 Moments and Laws of Large Numbers.- 6 Convergence Theorems.- 7 \u003ci\u003eL\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e-Spaces and the Radon–Nikodym Theorem.- 8 Conditional Expectations.- 9 Martingales.- 10 Optional Sampling Theorems.- 11 Martingale Convergence Theorems and Their Applications.- 12 Backwards Martingales and Exchangeability.- 13 Convergence of Measures.- 14 Probability Measures on Product Spaces.- 15 Characteristic Functions and the Central Limit Theorem.- 16 Infinitely Divisible Distributions.- 17 Markov Chains.- 18 Convergence of Markov Chains.- 19 Markov Chains and Electrical Networks.- 20 Ergodic Theory.- 21 Brownian Motion.- 22 Law of the Iterated Logarithm.- 23 Large Deviations.- 24 The Poisson Point Process.- 25 The Itô Integral.- 26 Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":51021119979863,"sku":"9783030564018","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030564018.jpg?v=1750785224"},{"product_id":"measure-and-integration-9789819725106","title":"Measure and Integration","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDesigned for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration. It acts as a pivotal link bridging the Riemann integral and the Lebesgue integral, with a primary focus on tracing the evolution of measure and integration from their historical roots. A distinctive feature of the book is meticulous guidance, providing a step-by-step journey through the subject matter, thus rendering complex concepts more accessible to beginners. A fundamental grasp of differential and integral calculus, as well as Riemann integration, is recommended to ensure a smoother comprehension of the material.   This textbook comprises 10 well-structured chapters, each thoughtfully organized to lead students from fundamental principles to advanced complexities. Beginning with the establishment of Lebesgue's measure on the real line and an introduction to measurable functions, the book then delves into exploring the cardinalities of various set classes. As readers progress, the subtleties of the Lebesgue integral emerge, showcasing its generalization of the Riemann integral and its unique characteristics in higher dimensions.   One of the book's distinctive aspects is its indepth comparison of the Lebesgue integral, improper Riemann integral, and Newton integral, shedding light on their distinct qualities and relative independence. Subsequent chapters delve into the realm of general measures, Lebesgue-Stieltje's measure, Hausdorff 's measure, and the concept of measure and integration in product spaces. Furthermore, the book delves into function spaces, such as 𝘓𝘱 spaces, and navigates the intricacies of signed and complex measures, providing students with a comprehensive foundation in this vital area of mathematics.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":51021460210007,"sku":"9789819725106","price":76.03,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819725106.jpg?v=1750786005"},{"product_id":"measure-theory-for-analysis-and-probability-9789819779284","title":"Measure Theory for Analysis and Probability","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Measure Theory: Why and What.- 2. Measures: Construction and Properties.- 3. Measurable Functions and Integration.- 4. Random Variables and Random Vectors.- 5. Product Spaces.- 6. Radon-Nikodym Theorem and Lp Spaces.- 7. Convergence and Laws of Large Numbers.- 8. Weak convergence and Central Limit Theorem.- 9. Conditioning: The Right Approach.- 10. Infinite Products.- 11. Brownian Motion: A Brief Journey.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":51021460242775,"sku":"9789819779284","price":54.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819779284.jpg?v=1750786005"},{"product_id":"the-analysis-of-fractional-differential-equations-an-application-oriented-exposition-using-differential-operators-of-caputo-type-9783642145735","title":"The Analysis of Fractional Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.   \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“This book treats a fast growing field of fractional differential equations, i.e., differential equations with derivatives of non-integer order. … The book consists of two parts, eight chapters, an appendix, references and an index. … The book is well written and easy to read. It could be used for, a course in the application of fractional calculus for students of applied mathematics and engineering.” (Teodor M. Atanacković, Mathematical Reviews, Issue 2011 j)\u003c\/p\u003e\u003cp\u003e“This monograph is intended for use by graduate students, mathematicians and applied scientists who have an interest in fractional differential equations. The Caputo derivative is the main focus of the book, because of its relevance to applications. … The monograph may be regarded as a fairly self-contained reference work and a comprehensive overview of the current state of the art. It contains many results and insights brought together for the first time, including some new material that has not, to my knowledge, appeared elsewhere.” (Neville Ford, Zentralblatt MATH, Vol. 1215, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFundamentals of Fractional Calculus.- Riemann-Liouville Differential and Integral Operators.- Caputo’s Approach.- Mittag-Leffler Functions.- Theory of Fractional Differential Equations.- Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations.- Single-Term Caputo Fractional Differential Equations: Basic Theory and Fundamental Results.- Single-Term Caputo Fractional Differential Equations: Advanced Results for Special Cases.- Multi-Term Caputo Fractional Differential Equations.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":51044620403031,"sku":"9783642145735","price":49.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783642145735.jpg?v=1750962203"},{"product_id":"lebesgues-theory-of-integration-9789819611683","title":"Lebesgues Theory of Integration","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe Integration before Riemann.- The Definition of Integral Given by Riemann.- Geometric Definition of the Integral.- The Functions of the Bounded Variation.- The Search for Primitive Functions.- The Integration Defined with the Help of Primitive Functions.- The Definite Integral of Summable Functions.- The Indefinite Integral of Summable Functions.- The Seach of Primitive Functions. The Existence of Derivatives.- The Totalisation.- The Integral of Steiltjes.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":51360833536343,"sku":"9789819611683","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819611683.jpg?v=1754128555"},{"product_id":"special-integrals-9789819775132","title":"Special Integrals","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eBinomial Series.- Trigonometrical Series.- Special Integrals.- Pseudo-Exponential Functions.- Series Sums using Special Integrals.- Solutions to Binomial Series.- Solutions to Trigonometrical Series.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":51535953690967,"sku":"9789819775132","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819775132.jpg?v=1755863907"},{"product_id":"lectures-on-convex-geometry-9783030501792","title":"Lectures on Convex Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a self-contained introduction to convex geometry in Euclidean space.  After covering the basic concepts and results, it develops Brunn–Minkowski  theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including  the isoperimetric inequality.  Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations.  Finally, an introduction to integral-geometric formulas in Euclidean space is provided.  The numerous exercises and the supplementary material at the end of each section form an essential part of the book.\u003c\/p\u003e  \u003cp\u003eConvexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry.\u003c\/p\u003e  \u003cp\u003ePaving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“‘Lectures on convex geometry’ is an excellent graduate book about convex geometry. … The book is very well-organized. … The presentation is clear, well-composed and illustrated. The problems at the end of each subchapter are carefully selected and revised. The whole text is readable, interesting and easy to learn from. … the book is excellent and it can serve the studies of the future generation students in convex geometry.” (Gergely Kiss, zbMATH 1487.52001, 2022)\u003cbr\u003e“The book is informative, very interesting, and mathematically accessible, and the authors have achieved the purpose that they outline above. As the title suggests, Lectures on convex geometry is well suited to be used as the prescribed textbook for graduate courses in convex geometry; this is because of its pedagogical style and the quality of the exercises. It will also be useful to students intending to pursue a research career in the area … .” (Daniel John Fresen, Mathematical Reviews, June, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Preliminaries and Notation.- 1. Convex Sets.- 2. Convex Functions.- 3. Brunn-Minkowski Theory.- 4. From Area Measures to Valuations.- 5. Integral Geometric Formulas.-6. Solutions of Selected Exercises.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":51585951531351,"sku":"9783030501792","price":54.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030501792.jpg?v=1756489904"},{"product_id":"calculus-with-applications-9781461479451","title":"Calculus With Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eBurstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“The book under review, a little over 500 pages co-authored with Maria Terrell, is a first-approximation to Lax’s dream come true: a ‘thorough revision’ of the 1976 Lax-Burstein-Lax. … This reviewer will attempt to use them as a pedagogical tool when teaching single-variable calculus or introductory analysis in the future. … It is filled with beautiful ideas that are elegantly explained and chock-full with problems that will enchant both the experienced teacher and the curious novice.” (Tushar Das, MAA Reviews, December, 2014)\u003c\/p\u003e“The text starts with introductory facts on real numbers, sequences and limits, followed by chapters aimed at differential and integral calculus. … The text is accompanied by a lot of worked examples, figures and applications. Together with detailed proofs of theorems this makes the text suitable also for self-study.” (Vladimír Janiš, zbMATH, 2014)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Numbers and Limits.- 2 Functions and Continuity.- 3 The Derivative and Differentiation.- 4 The Theory of Differentiable Functions.- 5 Applications of the Derivative.- 6 Integration.- 7 Methods for Integration.- 8 Approximation of Integrals.- 9 Complex Numbers.- 10 Differential Equations.- 11 Probability.- Answers to Selected Probems.- Index.","brand":"Springer","offers":[{"title":"Default Title","offer_id":51742559437143,"sku":"9781461479451","price":40.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461479451.jpg?v=1758385231"},{"product_id":"partial-differential-equations-and-geometric-measure-theory-cetraro-italy-2014-9783319740416","title":"Partial Differential Equations and Geometric Measure Theory: Cetraro, Italy 2014","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.  It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods.  The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered.  The lectures, given during the course \"Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area.  The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003eAlberto Farina and Enrico Valdinoci:\u003c\/i\u003eIntroduction.-\u003ci\u003eAlessio Figalli:\u003c\/i\u003eGlobal Existence for the Semi-Geostrophic Equations via Sobolev Estimates for Monge-Ampère.-\u003ci\u003eIreneo Peral Alonso: \u003c\/i\u003eOn Some Elliptic and Parabolic Equations Related to Growth Models.- \u003ci\u003eEnrico Valdinoci:\u003c\/i\u003e All Functions are (locally) S-harmonic (up to a small error) – and Applications\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":51742929486167,"sku":"9783319740416","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319740416.jpg?v=1758387422"},{"product_id":"time-fractional-differential-equations-a-theoretical-introduction-9789811590658","title":"Time-Fractional Differential Equations: A Theoretical Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. \u003c\/p\u003e  \u003cp\u003eThe fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media.\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003eThe studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eTo make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces.” (Syed Abbas, zbMATH 1485.34002, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":51743214109015,"sku":"9789811590658","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811590658.jpg?v=1758389503"},{"product_id":"delay-differential-equations-and-applications-to-biology-9789811606250","title":"Delay Differential Equations and Applications to Biology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The author provides extensive references for each chapter … . It offers a breadth of ideas and approaches that could be fertile ground for further research.” (Bill Satzer, MAA Reviews, December 12, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePart I Qualitative and Quantitative Features of Delay Differential Equations:\u003c\/b\u003e 1. Delay Differential Equations.- 2. Numerical Solutions of Delay Differential Equations.- 3. Stability Concepts of Numerical Solutions of Delay Differential Equations.- 4. Parameter Estimation with Delay Differential Equations.- \u003cb\u003ePart II Applications of Delay Differential Equations:\u003c\/b\u003e 5. Delay Differential Equations with Infectious Diseases.- 6. Delay Differential Equations with Cell Growth Dynamics.- 7. Delay Differential Equations with Tumour-Immure Interactions and External Treatments.- 8. Delay Differential Equations with Ecological Systems.- 9. Fractional-Order Delay Differential Equations with Applications.- 10. Sensitivity Analysis.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":51743214207319,"sku":"9789811606250","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811606250.jpg?v=1758389505"},{"product_id":"an-introduction-to-homogenization-17-oxford-lecture-series-in-mathematics-and-its-applications-9780198565543","title":"An Introduction to Homogenization 17 Oxford Lecture Series in Mathematics and Its Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe theory of homogenization replaces a real composite material with an imaginary homogeneous one, to describe the macroscopic properties of the composite using the properties of the microscopic structure. This work illustrates the relevant mathematics, logic and methodology with examples.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'serve as good textbook for a post-graduate course' ZAMM\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Weak and weak - convergence in Banach spaces ; 2. Rapidly oscillating periodic functions ; 3. Some classes of Sobolev spaces ; 4. Some variational elliptic problems ; 5. Examples of periodic composite materials ; 6. Homogenization of elliptic equations: the convergence result ; 7. The multiple-scale method ; 8. Tartar's method of oscillating test functions ; 9. The two-scale convergence method ; 10. Homogenization in linearized elasticity ; 11. Homogenization of the heat equation ; 12. Homogenization of the wave equation ; 13. General Approaches to the non-periodic case ; References","brand":"Oxford University Press, USA","offers":[{"title":"Default Title","offer_id":51766955049303,"sku":"9780198565543","price":155.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198565543.jpg?v=1758711829"},{"product_id":"heuns-differential-equations-9780198596950","title":"Heuns Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHeun''s equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger''s equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThere is a wealth of important results and open problems and the book is a welcome addition to the literature on these important special functions and their applications. * B D Sleeman, Zbl. Math. 847\/96. *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA. HEUN'S EQUATION  ; I: GENERAL AND POWER SERIES  ; II: HYPERGEOMETRIC FUNCTION SERIES  ; B. CONFLUENT HEUN EQUATION  ; C. DOUBLE CONFLUENT HEUN EQUATION  ; D. BICONFLUENT HEUN EQUATION  ; E. TRICONFLUENT HEUN EQUATION","brand":"Clarendon Press","offers":[{"title":"Default Title","offer_id":51766956032343,"sku":"9780198596950","price":162.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198596950.jpg?v=1758711861"},{"product_id":"the-numerical-solution-of-integral-equations-of-the-second-kind-4-cambridge-monographs-on-applied-and-computational-mathematics-series-number-4-9780521102834","title":"The Numerical Solution of Integral Equations of the Second Kind 4 Cambridge Monographs on Applied and Computational Mathematics Series Number 4","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving partic\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e' This outstanding monograph ... represents a major milestone in the list of books on the numerical solution of integral equations ... deserves to be on the shelf of any researcher and graduate student interested in the numerical solution of elliptic boundary-value problems.' H. Brunner, Mathematics Abstracts  'It will become the standard reference in the area.' Zietschrift fur Angwandte Mathematik und Physik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; 1. A brief discussion of integral equations; 2. Degenerate kernel methods; 3. Projection methods; 4. The Nystrom method; 5. Solving multivariable integral equations; 6. Iteration methods; 7. Boundary integral equations on a smooth planar boundary; 8. Boundary integral equations on a piecewise smooth planar boundary; 9. Boundary integral equations in three dimensions; Discussion of the literature; Appendix; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":51767596187991,"sku":"9780521102834","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780521102834.jpg?v=1758713938"},{"product_id":"classical-and-multilinear-harmonic-analysis-9780521882453","title":"Classical and Multilinear Harmonic Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis two-volume text in harmonic analysis is appropriate for advanced undergraduate students with a strong background in mathematical analysis and for beginning graduate students wishing to specialize in analysis. With numerous exercises and problems it is suitable for independent study as well as for use as a course text.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eReview of the set: 'The two-volume set under review is a worthy addition to this tradition from two of the younger generation of researchers. It is remarkable that the authors have managed to fit all of this into [this number of] smaller-than-average pages without omitting to provide motivation and helpful intuitive remarks. Altogether, these books are a most welcome addition to the literature of harmonic analysis.' Gerald B. Folland, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Acknowledgements; 1. Fourier series: convergence and summability; 2. Harmonic functions, Poisson kernel; 3. Conjugate harmonic functions, Hilbert transform; 4. The Fourier Transform on Rd and on LCA groups; 5. Introduction to probability theory; 6. Fourier series and randomness; 7. Calderón–Zygmund theory of singular integrals; 8. Littlewood–Paley theory; 9. Almost orthogonality; 10. The uncertainty principle; 11. Fourier restriction and applications; 12. Introduction to the Weyl calculus; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":51767759929687,"sku":"9780521882453","price":59.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780521882453.jpg?v=1758714758"},{"product_id":"regularization-of-inverse-problems-mathematics-and-its-applications-closed-375-9780792361404","title":"Regularization of Inverse Problems Mathematics and its Applications closed 375","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cstrong\u003e`\u003c\/strong\u003eIt is written in a very clear style, the material is  well organized, and there is an extensive bibliography with 290 items.  There is no doubt that this book belongs to the modern standard  references on ill-posed and inverse problems. It can be recommended  not only to mathematicians interested in this, but to students with a  basic knowledge of functional analysis, and to scientists and  engineers working in this field.\u003cstrong\u003e'\u003c\/strong\u003e \u003cbr\u003e  \u003cstrong\u003eMathematical Reviews Clippings, 97k\u003c\/strong\u003e \u003cbr\u003e  \u003cstrong\u003e`\u003c\/strong\u003e... it will be an extremely valuable tool for researchers in  the field, who will find under the same cover and with unified  notation material that is otherwise scattered in extremely diverse  publications.\u003cstrong\u003e'\u003c\/strong\u003e \u003cbr\u003e  \u003cstrong\u003eSIAM Review, 41:2 (1999)\u003c\/strong\u003e \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface. 1. Introduction: Examples of Inverse Problems.  2. Ill-Posed Linear Operator Equations. 3. Regularization  Operators. 4. Continuous Regularization Methods. 5.  Tikhonov Regularization. 6. Iterative Regularization Methods.  7. The Conjugate Gradient Method. 8. Regularization with  Differential Operators. 9. Numerical Realization. 10.  Tikhonov Regularization of Nonlinear Problems. 11. Iterative  Methods for Nonlinear Problems. A. Appendix: A.1. Weighted  Polynomial Minimization Problems. A.2. Orthogonal Polynomials.  A.3. Christoffel Functions. Bibliography. Index.","brand":"Springer","offers":[{"title":"Default Title","offer_id":51768045535575,"sku":"9780792361404","price":132.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780792361404.jpg?v=1758716065"},{"product_id":"semiconcave-functions-hamiltonjacobi-equations-and-optimal-control-9780817643362","title":"Semiconcave Functions HamiltonJacobi Equations and Optimal Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA comprehensive exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems. It is suitable for graduate students and researchers in optimal control, the calculus of variations, and PDEs.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"The main purpose of this book is to provide a systematic study of the notion of semiconcave functions, as well as a presentation of mathematical fields in which this notion plays a fundamental role. Many results are extracted from articles by the authors and their collaborators, with simplified—and often new—presentation and proofs.... One of the most attractive features of this book is the interplay between several fields of mathematical analysis.... Despite the many topics addressed in the book, the required mathematical background for reading it is limited because all the necessary notions are not only recalled, but also carefully explained, and the main results proved.\u003c\/p\u003e \u003cp\u003eThe book will be found very useful by experts in nonsmooth analysis, nonlinear control theory and PDEs, in particular, as well as by advanced graduate students in this field. They will appreciate the many detailed examples, the clear proofs and the elegant style of presentation, the fairly comprehensive and up-to-date bibliography and the very pertinent historical and bibliographical comments at the end of each chapter.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—Mathematical Reviews\u003c\/strong\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA Model Problem.- Semiconcave Functions.- Generalized Gradients and Semiconcavity.- Singularities of Semiconcave Functions.- Hamilton-Jacobi Equations.- Calculus of Variations.- Optimal Control Problems.- Control Problems with Exit Time.","brand":"Birkhauser Boston","offers":[{"title":"Default Title","offer_id":51768179654999,"sku":"9780817643362","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817643362.jpg?v=1758716730"},{"product_id":"troilus-and-cressida-the-new-cambridge-shakespeare-9781107031821","title":"Troilus and Cressida The New Cambridge Shakespeare","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional CalderÃnâZygmund and LittlewoodâPaley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; CoifmanâMeyer theory; Carleson's resolution of the Lusin conjecture; CalderÃn's commutators and the Cauchy integral on Lipschitz curves. T\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eReview of the set: 'The two-volume set under review is a worthy addition to this tradition from two of the younger generation of researchers. It is remarkable that the authors have managed to fit all of this into [this number of] smaller-than-average pages without omitting to provide motivation and helpful intuitive remarks. Altogether, these books are a most welcome addition to the literature of harmonic analysis.' Gerald B. Folland, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Acknowledgements; 1. Leibniz rules and gKdV equations; 2. Classical paraproducts; 3. Paraproducts on polydiscs; 4. Calderón commutators and the Cauchy integral; 5. Iterated Fourier series and physical reality; 6. The bilinear Hilbert transform; 7. Almost everywhere convergence of Fourier series; 8. Flag paraproducts; 9. Appendix: multilinear interpolation; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":51768966840663,"sku":"9781107031821","price":59.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781107031821.jpg?v=1758719191"},{"product_id":"concrete-functional-calculus-springer-monographs-in-mathematics-9781441969491","title":"Concrete Functional Calculus Springer Monographs in Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003eConcrete Functional Calculus\u003c\/i\u003e focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“This monograph is a thorough and masterful work on non-linear analysis designed to be read and studied by graduate students and professional mathematical researchers. The overall perspective and choice of material is highly novel and original. … It is a unique account of some key areas of modern analysis which will surely turn out to be invaluable for many researchers in this and related areas.” (David Applebaum, The Mathematical Gazette, Vol. 98 (541), March, 2014)\u003c\/p\u003e\u003cp\u003e“The present monograph is quite extensive and interesting. It is divided into twelve chapters on different topics on Functional calculus and an appendix on non-atomic measure spaces. … The book has many historical comments and remarks which clarify the developments of the theory. It has also an extensive bibliography with 258 references. … will be very useful for all interested readers in Real-Functional Analysis and Probability.” (Francisco L. Hernandez, The European Mathematical Society, January, 2012)\u003c\/p\u003e\u003cp\u003e“The monograph under review aims at analyzing properties such as Hölder continuity, differentiability and analyticity of various types of nonlinear operators which arises in the study of differential and integral equations and in applications to problems of statistics and probability. … this is an interesting book which contains a lot of material.” (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2012 e)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1 Introduction and Overview.- 2 Definitions and Basic Properties of Extended Riemann-Stieltjes integrals.- 3 Phi-variation and p-variation; Inequalities for Integrals.- 4 Banach Algebras.- 5 Derivatives and Analyticity in Normed Spaces.- 6 Nemytskii Operators on Function Spaces.- 7 Nemytskii Oerators on Lp Spaces.- 8 Two-Function Composition.- 9 Product Integration.- 10 Nonlinear Differential and Integral Equations.- 11 Fourier Series.- 12 Stochastic Processes and Phi-Variation.- Appendix Nonatomic Measure Spaces.- References.- Subject Index.- Author Index.- Index of Notation.","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":51769662898519,"sku":"9781441969491","price":123.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441969491.jpg?v=1758722125"},{"product_id":"stochastic-processes-inference-theory-9783319121710","title":"Stochastic Processes - Inference Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics.\u003c\/p\u003e\u003cp\u003eThe first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“A wonderful text with a very high pedagogical and scientific quality, on inference theory in stochastic processes, important for researchers in probability theory, mathematical statistics and electrical and information theory.” (Prof. Dr. Manuel Alberto M. Ferreira, Acta Scientiae et Intellectus, Vol. 2 (1), 2016)\u003c\/p\u003e\u003cp\u003e“This book is the revised and enlarged edition of the author's original text … . The book is well written and will be of interest for researchers in probability theory and mathematical statistics.” (N. G. Gamkrelidze, zbMATH 1341.62036, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1.Introduction and Preliminaries.- 2.Some Principles of Hypothesis Testing.- 3.Parameter Estimation and Asymptotics.- 4.Inferences for Classes of Processes.- 5.Likelihood Ratios for Processes.- 6.Sampling Methods for Processes.- 7.More on Stochastic Inference.- 8.Prediction and Filtering of Processes.- 9.Nonparametric Estimation for Processes.- Bibliography.- Index.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":51772006170967,"sku":"9783319121710","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319121710.jpg?v=1758729911"},{"product_id":"analysis-ii-differential-and-integral-calculus-fourier-series-holomorphic-functions-9783540209218","title":"Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFunctions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eFrom the reviews of the original French edition:\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"... The content is quite classical ... [...] The treatment is less classical: precise although unpedantic (rather far from the definition-theorem-corollary-style), it contains many interesting commentaries of epistemological, pedagogical, historical and even political nature. [...] The author gives frequent interesting hints on recent developments of mathematics connected to the concepts which are introduced. The Introduction also contains comments that are very unusual in a book on mathematical analysis, going from pedagogy to critique of the French scientific-military-industrial complex, but the sequence of ideas is introduced in such a way that readers are less surprised than they might be.\u003cbr\u003e\u003cem\u003eJ. Mawhin in Zentralblatt Mathematik (1999)\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eDifferential and Integral Calculus.- The Riemann Integral.- Integrability Conditions.- The “Fundamental Theorem” (FT).- Integration by parts.- Taylor’s Formula.- The change of variable formula.- Generalised Riemann integrals.- Approximation Theorems.- Radon measures in ? or ?.- Schwartz distributions.- Asymptotic Analysis.- Truncated expansions.- Summation formulae.- Harmonic Analysis and Holomorphic Functions.- Analysis on the unit circle.- Elementary theorems on Fourier series.- Dirichlet’s method.- Analytic and holomorphic functions.- Harmonic functions and Fourier series.- From Fourier series to integrals.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":51772020359511,"sku":"9783540209218","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540209218.jpg?v=1758729966"},{"product_id":"integration-chapitres-7-a-8-9783540353249","title":"Intégration: Chapitres 7 à 8","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eCe volume du Livre d’Intégration, sixième Livre du traité, traite de l’intégration sur les groupes localement compacts et de ses applications. Les notions introduites, telles que les mesures de Haar et le produit de convolution, sont à la base de l’analyse harmonique. Il comprend les chapitres : -1. Mesure de Haar ; -2. Convolution et représentations.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eMesure de Haar.- Convolution et Représentation.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":51772022423895,"sku":"9783540353249","price":39.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540353249.jpg?v=1758729975"},{"product_id":"hamiltonian-methods-in-the-theory-of-solitons-9783540698432","title":"Hamiltonian Methods in the Theory of Solitons","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Nonlinear Schrödinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples and Their General Properties.- Fundamental Continuous Models.- Fundamental Models on the Lattice.- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models.- Conclusion.- Conclusion. ","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":51772025176407,"sku":"9783540698432","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540698432.jpg?v=1758729984"},{"product_id":"analysis-iii-9783764374792","title":"Analysis III","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e“This third volume contains an introduction to Bochner\u003cb\u003e-\u003c\/b\u003eLebesgue integral theory and differential forms’ calculus on smooth manifolds. … The text is clear and understandable and yet it provides a very detailed presentation of the covered topics from an advanced and abstract point of view. The reader can easily develop deep intuitive ideas following the numerous examples, exercises and pictures that are included.” (Tihomir Gyulov, Zentralblatt MATH, Vol. 1187, 2010)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eElements of measure theory.- Integration theory.- Manifolds and differential forms.- Integration on manifolds.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":51772066890071,"sku":"9783764374792","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783764374792.jpg?v=1758730135"},{"product_id":"mathematical-theory-of-feynman-path-integrals-an-introduction-9783540769545","title":"Mathematical Theory of Feynman Path Integrals: An Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.\u003c\/p\u003e\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\u003c\/p\u003e\u003cp\u003e\"The second edition (from 2008) contains a large additional chapter … entitled ‘Some Recent Developments’, where alternative attempts at a rigourous formalism are presented, as well as recent applications. Summarizing, this is a good and insightful book for those familiar with path integrals and curious about the mathematic foundations of path integration.\" (Jacques Tempere, Belgian Physical Society Magazine, Issue 2, June, 2009)\u003c\/p\u003e\u003cp\u003e“The new edition goes way beyond the habitual corrections and additions … . It is good to have this new book. Not only for the more recent results it contains, but also as a point of departure for so many questions that are still open in the realm of infinite dimensional oscillatory integrals.” (Ludwig Streit, Zentralblatt MATH, Vol. 1222, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Fresnel Integral of Functions on a Separable Real Hilbert Space.- The Feynman Path Integral in Potential Scattering.- The Fresnel Integral Relative to a Non-singular Quadratic Form.- Feynman Path Integrals for the Anharmonic Oscillator.- Expectations with Respect to the Ground State of the Harmonic Oscillator.- Expectations with Respect to the Gibbs State of the Harmonic Oscillator.- The Invariant Quasi-free States.- The Feynman History Integral for the Relativistic Quantum Boson Field.- Some Recent Developments.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":52091505901911,"sku":"9783540769545","price":32.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540769545.jpg?v=1762274865"},{"product_id":"infinite-interval-problems-for-differential-difference-and-integral-equations-9789401038348","title":"Infinite Interval Problems for Differential, Difference and Integral Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eInfinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom­ ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cstrong\u003e'\u003c\/strong\u003ethe monograph is well written and will be of interest  for mathematicians and graduate students with research interest in  applied mathematics.\u003cstrong\u003e'\u003c\/strong\u003e\u003cbr\u003e  \u003cstrong\u003eZentral Blatt Mathematik, 988 (2002)\u003c\/strong\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface. 1. Second Order Boundary Value Problems.  2. Higher Order Boundary Value Problems. 3. Continuous  Systems. 4. Integral Equations. 5. Discrete Systems.  6. Equations in Banach Spaces. 7. Multivalued Equations.  8. Equations on Time Scales. Subject Index.","brand":"Springer","offers":[{"title":"Default Title","offer_id":52091874804055,"sku":"9789401038348","price":85.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789401038348.jpg?v=1762276108"},{"product_id":"mathematical-economics-of-general-equilibrium-9789819694969","title":"Mathematical Economics of General Equilibrium","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1 Introduction.- 2 Notation in Economic Analysis.- Part I Mathematical Preliminaries.- 3 Some Basic Facts and Properties in Mathematical Analysis.- Part II Foundations of Theoretical Economic Analysis.- 4 Basic Concepts of Equilibrium Analysis.- 5 Mathematical Structures on the Space of Agents’ Characteristics.- 6 Individual Demands.- 7 Economies with a Measure Space of Consumers.- 8 Walrasian Equilibria of Economies.- 9 Production in Economies.- 10 Edgeworth Equilibria as the Core of Economies.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":52091903738199,"sku":"9789819694969","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819694969.jpg?v=1762276215"}],"url":"https:\/\/bookcurl.com\/collections\/integral-calculus-and-equations.oembed?page=3","provider":"Book Curl","version":"1.0","type":"link"}