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: Alexander S. Holevo Название: Quantum Systems, Channels, Information: A Mathematical Introduction ISBN: 311027325X ISBN-13(EAN): 9783110273250 Издательство: Walter de Gruyter Цена: 16916.00 р. 24166.00-30% Наличие на складе: Есть (1 шт.) Описание: The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics. Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information. Quantum cryptography allows for secure communication of classified information. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world.The past years were marked with impressive progress made by several researchers in solution of some difficult problems, in particular, the additivity of the entropy characteristics of quantum channels. This suggests a need for a book that not only introduces the basic concepts of quantum information theory, but also presents in detail some of the latest achievements.
Автор: Bocklandt Raf Название: A Gentle Introduction to Homological Mirror Symmetry ISBN: 110848350X ISBN-13(EAN): 9781108483506 Издательство: Cambridge University Press Рейтинг: Цена: 25553.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Originating in mathematical physics, homological mirror symmetry reveals deep connections between different areas of geometry and algebra. This book, which is aimed at graduate students, offers a self-contained and accessible introduction to the subject from the perspective of representation theory of algebras and quivers.
Автор: Edoardo Benvenuto Название: An Introduction to the History of Structural Mechanics ISBN: 1461277450 ISBN-13(EAN): 9781461277453 Издательство: Springer Рейтинг: Цена: 15672.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Theorists know that when, at last, theories began to appear, architects distrusted them, partly because they often disregarded details of importance in actual construction, partly because nobody but a mathematician could understand the aim and func- tion of a mathematical theory designed to represent an aspect of nature.
Автор: Bowman Gregory R. Название: Introduction to Markov State Models and Their Application to ISBN: 9400776055 ISBN-13(EAN): 9789400776050 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces the mathematical foundations of Markov models and details how they can be used to analyze simulations and drive efficient simulations. It also presents some of the insights these models have yielded in a variety of applications.
Автор: Ewald Balcar; Stephen W. Lovesey Название: Introduction to the Graphical Theory of Angular Momentum ISBN: 3642260608 ISBN-13(EAN): 9783642260605 Издательство: Springer Рейтинг: Цена: 30745.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Application of quantum mechanics in physics and chemistry often entails manipulation and evaluation of sums and products of coupling coefficients for the theory of angular momentum. Here is the first step-by-step exposition of a graphical method grounded in established work.
Автор: Stuart Raby Название: Introduction to the Standard Model and Beyond ISBN: 1108494196 ISBN-13(EAN): 9781108494199 Издательство: Cambridge Academ Рейтинг: Цена: 10454.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Written for a two-semester graduate course on the Standard Model, this text develops a practical understanding of the theoretical concepts, to prepare students to enter particle physics research. Taking a historical approach, it presents quantum field theory and symmetries as the necessary tools for describing and understanding the Standard Model.
Автор: Yoshiaki Tanii Название: Introduction to Supergravity ISBN: 4431548270 ISBN-13(EAN): 9784431548270 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explains the basic ideas of supergravity, collecting the relevant formulae in one place. Covers vielbein formulation of gravity; supergravities in four dimensions; superalgebras and supermultiplets; supergravities in higher dimensions and more.
Автор: Blyth, Stephen Название: An Introduction to Quantitative Finance ISBN: 019966658X ISBN-13(EAN): 9780199666584 Издательство: Oxford Academ Рейтинг: Цена: 10138.00 р. Наличие на складе: Поставка под заказ.
Описание: The quantitative nature of complex financial transactions makes them a fascinating subject area for mathematicians of all types. This book gives an insight into financial engineering while building on introductory probability courses by detailing one of the most fascinating applications of the subject.
Автор: Nolte David D Название: Introduction to Modern Dynamics ISBN: 0198844638 ISBN-13(EAN): 9780198844631 Издательство: Oxford Academ Рейтинг: Цена: 7602.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Presents a unifying approach to the physics of chaos, nonlinear systems, dynamic networks, evolutionary dynamics, econophysics, and the theory of relativity. Each chapter has many worked examples and simple computer simulations that allow the student to explore the rich phenomena of nonlinear physics.
Автор: Aldrovandi Ruben, Da Rocha Jr Roldao Название: A Gentle Introduction to Knots, Links and Braids ISBN: 9811248486 ISBN-13(EAN): 9789811248481 Издательство: World Scientific Publishing Рейтинг: Цена: 21404.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles -- the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems -- are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
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