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: Fuente, Angel de la. Название: Mathematical methods and models for economists ISBN: 0521585295 ISBN-13(EAN): 9780521585293 Издательство: Cambridge Academ Рейтинг: Цена: 8554.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is intended as a textbook for a first-year PhD course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics.
Описание: A solutions manual to accompany An Introduction to Discrete Mathematical Modeling with Microsoft(R) Office Excel(R)
With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft(R) Office Excel(R)guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques.
The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft(R) Office Excel(R) also features:
A modular organization that, after the first chapter, allows readers to explore chapters in any order
Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data
Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt
References throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study
Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material
Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug's therapeutic window
A companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor's manual with solutions to all homework problems, project ideas, and a test bank
Описание: The book introduces the principles of mathematical modeling in science, engineering, and social science as well as basic skills of computer programming. The book is aimed at majors in STEM disciplines that need to understand how to create, analyze, and test mathematical models.
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.
Описание: This book describes a system of mathematical models and methods that can be used to analyze real economic and managerial decisions and to improve their effectiveness.
Описание: Provides an introduction to probability theory and its applications.
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.
Описание: This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given.
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