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: Crockett, Robin (university Of Northampton) Название: A Primer on Fourier Analysis for the Geosciences ISBN: 1316600246 ISBN-13(EAN): 9781316600245 Издательство: Cambridge Academ Рейтинг: Цена: 6019.00 р. Наличие на складе: Поставка под заказ.
Описание: An intuitive introduction to basic Fourier theory, with an emphasis on geoscience applications. Numerous worked examples from R are used to illustrate the theory, making this an ideal practical guide for graduate students and researchers who are using time-series analysis to quantify periodic features in geoscience data.
Автор: Colm T. Whelan Название: A First Course in Mathematical Physics ISBN: 3527413332 ISBN-13(EAN): 9783527413331 Издательство: Wiley Рейтинг: Цена: 6328.00 р. Наличие на складе: Поставка под заказ.
Описание: The book assumes next to no prior knowledge of the topic. The first part introduces the core mathematics, always in conjunction with the physical context. In the second part of the book, a series of examples showcases some of the more conceptually advanced areas of physics, the presentation of which draws on the developments in the first part.
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: Blinder, Seymour Название: Mathematical Physics in Theoretical Chemistry ISBN: 0128136510 ISBN-13(EAN): 9780128136515 Издательство: Elsevier Science Рейтинг: Цена: 26444.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The field of theoretical and computational chemistry is rapidly evolving as new algorithms and techniques are developed. Mathematical Physics in Theoretical Chemistry deals with the important topics in theoretical and computational chemistry, presenting them in a unified and efficient mannaer. Topics covered include density functional theory, computational methods in biological chemistry, and Hartree-Fock methods.
Mathematical Physics in Theoretical Chemistry is the second volume in the Developments in Physical & Theoretical Chemistry series. Each volume in the series contains highlights of the major advances and developments in research and serves as a basis for advanced study. With a multi-disciplinary and encompassing structure guided by a highly experienced editor, the series is designed to enable researchers in both academia and industry to efficiently keep abreast of developments in physical and theoretical chemistry.
Brings together in one volume the most important aspects of recent advances in theoretical and computational chemistry
Topics covered include computational methods for small molecules, density-functional methods, and computational chemistry on personal and quantum computers
Presents cutting-edge developments in theoretical and computational chemistry applicable to graduate students and research professionals in chemistry, physics, materials science, and biochemistry
Автор: Kuramoto Название: Dynamics of One-Dimensional Quantum Systems ISBN: 1107424720 ISBN-13(EAN): 9781107424722 Издательство: Cambridge Academ Рейтинг: Цена: 8870.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This self-contained book provides graduate students and new researchers with an intuitive understanding of exact dynamical properties of one-dimensional quantum systems. Its concise and accessible accounts of powerful concepts allow non-specialist readers to understand the physics of one-dimensional quantum systems through the simplest model.
Автор: Sahrling, Mikael, Название: Fast techniques for integrated circuit design / ISBN: 1108498450 ISBN-13(EAN): 9781108498456 Издательство: Cambridge Academ Рейтинг: Цена: 15365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Learn how to use estimation techniques to solve integrated circuit (IC) design problems, accelerate the design process, and enhance understanding of complex systems with this step-by-step guide. Using numerous real-world application examples, it is ideal for both early-career and established professionals and researchers, and graduate students, working in IC design.
Описание: Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra and measure angle.
Описание: An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts.
Автор: Sokolov, Vladimir V (landau Ins For Theoretical Physics, Russia) Название: Algebraic structures in integrability: foreword by victor kac ISBN: 9811219648 ISBN-13(EAN): 9789811219641 Издательство: World Scientific Publishing Рейтинг: Цена: 19800.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Relationships of the theory of integrable systems with various branches of mathematics are extremely deep and diverse. On the other hand, the most fundamental exactly integrable systems often have applications in theoretical physics. Therefore, many mathematicians and physicists are interested in integrable models.The book is intelligible to graduate and PhD students and can serve as an introduction to separate sections of the theory of classical integrable systems for scientists with algebraic inclinations. For the young, the book can serve as a starting point in the study of various aspects of integrability, while professional algebraists will be able to use some examples of algebraic structures, which appear in the theory of integrable systems, for wide-ranging generalizations.The statements are formulated in the simplest possible form. However, some ways of generalization are indicated. In the proofs, only essential points are mentioned, while for technical details, references are provided. The focus is on carefully selected examples. In addition, the book proposes many unsolved problems of various levels of complexity. A deeper understanding of every chapter of the book may require the study of more rigorous and specialized literature.
Автор: Starkovich Steven P. Название: The Structures of Mathematical Physics: An Introduction ISBN: 303073448X ISBN-13(EAN): 9783030734480 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics.
Автор: Jensen, Henrik Jeldtoft (imperial College London) Название: Complexity science ISBN: 1108834760 ISBN-13(EAN): 9781108834766 Издательство: Cambridge Academ Рейтинг: Цена: 6334.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introductory textbook provides detailed coverage of the rapidly growing field of complexity science and accommodates readers from a wide variety of backgrounds, and with varying levels of mathematical skill. The book contains a broad range of end of chapter problems and extended projects, with solutions available to instructors online.
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