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: Grimmett Название: Probability and Random Processes 3ed ISBN: 0198572220 ISBN-13(EAN): 9780198572220 Издательство: Oxford Academ Рейтинг: Цена: 7206.00 р. Наличие на складе: Поставка под заказ.
Описание: Love Your Home is an inspiring and thought-provoking sourcebook of ideas for home design. It explores the concept of `home` and its role as a private retreat and sanctuary, as well as a social hub for entertaining and the centre of family life. Provides an introduction to probability and random processes and their practical applications. This third edition emphasizes modeling and understanding rather than abstraction. Many important random processes are developed in the text through examples. It includes exercises and problems, with solutions provided in the companion volume.
Автор: Chaumont Название: Exercises in Probability ISBN: 1107606551 ISBN-13(EAN): 9781107606555 Издательство: Cambridge Academ Рейтинг: Цена: 8870.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Ideal for independent study or as a companion to a course in advanced probability theory, this book now includes over 100 exercises. In each case, the authors provide a detailed solution and references for preliminary and further reading. Insightful notes help to set the exercises in context.
Описание: Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.
Описание: This handbook brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians.
Автор: Grimmett, Geoffrey Stirzaker, David Название: One thousand exercises in probability ISBN: 0198572212 ISBN-13(EAN): 9780198572213 Издательство: Oxford Academ Рейтинг: Цена: 7522.00 р. Наличие на складе: Поставка под заказ.
Описание: Provides a selection of informative problems, together with their solution. This edition of the popular exercise manual includes modeling and many applications of probability theory, as well as theoretical aspects. There are questions at all ability levels, the majority being of elementary or intermediate standard.
Автор: Leadbetter Название: A Basic Course in Measure and Probability ISBN: 1107652529 ISBN-13(EAN): 9781107652521 Издательство: Cambridge Academ Рейтинг: Цена: 7286.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This concise introduction covers all of the measure theory and probability most useful for statisticians. Originating from the authors` own graduate course, it is perfect for a two-term course or for self-study. It is especially useful to graduate students in related fields who want to shore up their mathematical foundation.
Автор: Myers Raymond H. Название: Response Surface Methodology ISBN: 1118916018 ISBN-13(EAN): 9781118916018 Издательство: Wiley Рейтинг: Цена: 20109.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Praise for the Third Edition: This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM.
Автор: Kay Название: Intuitive Probability and Random Processes using MATLAB® ISBN: 0387241574 ISBN-13(EAN): 9780387241579 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offering an introduction to probability and random processes, this book merges theory with practice. It is suitable for undergraduate and first-year graduate students in engineering, practicing engineers as well as others having appropriate mathematical background.
Описание: Combining theory with numerous MATLAB based examples, this text provides a clear and systematic treatment of the mathematical and physical foundations of imaging and wavefield inversion. Key areas of discussion include Green function and the concept of field time reversal. It will appeal to graduate students and researchers alike.
Автор: Koralov Название: Theory of Probability and Random Processes ISBN: 3540254846 ISBN-13(EAN): 9783540254843 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of the content of this bookIt is structured in two parts: the first part providing a detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. The second part includes the theory of stationary random processes, martingales, generalized random processes, Brownian motion, stochastic integrals, and stochastic differential equations. One section is devoted to the theory of Gibbs random fields.This material is essential to many undergraduate and graduate courses. The book can also serve as a reference for scientists using modern probability theory in their research.
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