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
Описание: The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. This book is the new edition of the original two volume book, under the same title, published in 1994.
Описание: This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop.
Автор: Foucart Simon Название: Mathematical Introduction to Compressive Sensing ISBN: 0817649476 ISBN-13(EAN): 9780817649470 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
Introduction to Computational Modeling Using C and Open-Source Tools presents the fundamental principles of computational models from a computer science perspective. It explains how to implement these models using the C programming language. The software tools used in the book include the Gnu Scientific Library (GSL), which is a free software library of C functions, and the versatile, open-source GnuPlot for visualizing the data. All source files, shell scripts, and additional notes are located at ksuweb.kennesaw.edu/ jgarrido/comp_models.
The book first presents an overview of problem solving and the introductory concepts, principles, and development of computational models before covering the programming principles of the C programming language. The author then applies programming principles and basic numerical techniques, such as polynomial evaluation, regression, and other numerical methods, to implement computational models. He also discusses more advanced concepts needed for modeling dynamical systems and explains how to generate numerical solutions. The book concludes with the modeling of linear optimization problems.
Emphasizing analytical skill development and problem solving, this book helps you understand how to reason about and conceptualize the problems, generate mathematical formulations, and computationally visualize and solve the problems. It provides you with the foundation to understand more advanced scientific computing, including parallel computing using MPI, grid computing, and other techniques in high-performance computing.
Автор: K. Wickwire; L. Schmetterer Название: Introduction to Mathematical Statistics ISBN: 3642655440 ISBN-13(EAN): 9783642655449 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: to Mathematical Statistics Translated from the German by Kenneth Wickwire Springer-Verlag Berlin Heidelberg New York 1974 Leopold Schmetterer Professor of Statistics and Mathematics at the University of Vienna Translator: Kenneth Wickwire Department of Mathematics, University of Manchester Title of the German Original Edition: Einfiihrung in die mathematische Statistik, 2. verbesserte und wesentlich erweiterte Auflage Springer-Verlag Wien New York 1966 With 11 figures AMS Subject Classification (1970): 62-01, 62 Axx, 62 Bxx, 62 Cxx, 62D03, 62 Exx, 62 Fxx, 62 Gxx, 62 Hxx ISBN-13: 978-3-642-65544-9 e-ISBN-13: 978-3-642-65542-5 DOl: 10. 1007/978-3-642-65542-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. (c) by Springer-Verlag Berlin- Heidelberg 1974. Library of Congress Catalog Card Number 73-15290. Softcover reprint of the hardcover 1 st edition 1974 Bookbinding: Konrad Triltsch, Wiirzburg. Preface I have used the opportunity of the second edition of the German version being translated into English to alter and improve some details. Of course I tried to correct misprints and errata of the original version. Moreover some proofs have been slightly changed and I hope thereby improved.
Описание: Provides an introduction to probability theory and its applications.
Автор: Hoffstein, Jeffrey Pipher, Jill Silverman, J. H. Название: Introduction to mathematical cryptography ISBN: 1441926747 ISBN-13(EAN): 9781441926746 Издательство: Springer Рейтинг: Цена: 5723.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics. It includes exercises and examples at the end of each section.
Описание: A monograph to present a unified approach to using mathematical models in the study of qualitative and quantitative regularities of immune response dynamics in infectious diseases within individual organisms. It is intended for a range of mathematicians and specialists in immunology and infectious diseases.
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