This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Автор: Goldreich, Oded Название: Foundations of cryptography: volume 2, basic applications ISBN: 052111991X ISBN-13(EAN): 9780521119917 Издательство: Cambridge Academ Рейтинг: Цена: 9029.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Building on the basic tools presented in the first volume, this second volume of Foundations of Cryptography contains a rigorous and systematic treatment of three basic applications: Encryption, Signatures, and General Cryptographic Protocols. It is suitable for use in a graduate course on cryptography and as a reference book for experts.
Автор: Chi Tat Chong, Liang Yu Название: Recursion Theory: Computational Aspects of Definability ISBN: 3110275554 ISBN-13(EAN): 9783110275551 Издательство: Walter de Gruyter Цена: 20712.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory.The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
Автор: Murray, James D. Название: Mathematical Biology I. An Introduction ISBN: 1475777094 ISBN-13(EAN): 9781475777093 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others.
Описание: This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences.
Автор: Bernhard Steffen; Oliver R?thing; Michael Huth Название: Mathematical Foundations of Advanced Informatics ISBN: 3319683969 ISBN-13(EAN): 9783319683966 Издательство: Springer Рейтинг: Цена: 4611.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A core principle throughout is invariance, which the authors consider a key for the mastery of change, whether in the form of extensions, transformations, or abstractions.This textbook is suitable for undergraduate and graduate courses in computer science and for self-study.
Автор: Bender, Carl M. (washington University, Usa) Orsza Название: Advanced mathematical methods for scientists and engineers ISBN: 1441931872 ISBN-13(EAN): 9781441931870 Издательство: Springer Рейтинг: Цена: 10335.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions.
Автор: Powers, Joseph M. (University of Notre Dame, Indiana) Sen, Mihir (University of Notre Dame, Indiana) Название: Mathematical Methods in Engineering ISBN: 1107037042 ISBN-13(EAN): 9781107037045 Издательство: Cambridge Academ Рейтинг: Цена: 10138.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is designed for engineering graduate students. It connects mathematics to a variety of methods used for engineering problems by walking the reader stepwise through examples that have been worked in detail, followed by numerous homework problems to reinforce learning and connect the subject matter to engineering applications.
Can you really keep your eye on the ball? How is massive data collection changing sports?
Sports science courses are growing in popularity. The author's course at Roanoke College is a mix of physics, physiology, mathematics, and statistics. Many students of both genders find it exciting to think about sports. Sports problems are easy to create and state, even for students who do not live sports 24/7. Sports are part of their culture and knowledge base, and the opportunity to be an expert on some area of sports is invigorating. This should be the primary reason for the growth of mathematics of sports courses: the topic provides intrinsic motivation for students to do their best work.
From the Author:
The topics covered in Sports Science and Sports Analytics courses vary widely. To use a golfing analogy, writing a book like this is like hitting a drive at a driving range; there are many directions you can go without going out of bounds. At the driving range, I pick out a small target to focus on, and that is what I have done here. I have chosen a sample of topics I find very interesting. Ideally, users of this book will have enough to choose from to suit whichever version of a sports course is being run.
The book is very appealing to teach from as well as to learn from. Students seem to have a growing interest in ways to apply traditionally different areas to solve problems. This, coupled with an enthusiasm for sports, makes Dr. Minton's book appealing to me.--Kevin Hutson, Furman University
Автор: Watrous, John (university Of Waterloo, Ontario) Название: The theory of quantum information ISBN: 1107180562 ISBN-13(EAN): 9781107180567 Издательство: Cambridge Academ Рейтинг: Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Intended for graduate students and researchers, this book presents a formal development of the mathematical theory of quantum information. Largely self-contained, with clear proofs and a wide range of exercises, it will help the reader grasp the fundamental facts and techniques that form the mathematical foundations of the subject.
Автор: Kot, Mark, Название: Elements of Mathematical Ecology ISBN: 0521001501 ISBN-13(EAN): 9780521001502 Издательство: Cambridge Academ Рейтинг: Цена: 13779.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: An introduction to classical and modern mathematical models, methods, and issues in population ecology. Includes numerous line diagrams, relevant problems and supplementary mathematical and historical material that enhances understanding.
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