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This textbook is aimed at advanced undergraduate and graduate students interested in learning the fundamental mathematical concepts and tools widely used in different areas of physics. The author draws on a vast teaching experience, and presents a comprehensive and self-contained text which explains how mathematics intertwines with and forms an integral part of physics in numerous instances. Rather than emphasizing rigorous proofs of theorems, specific examples and physical applications (such as fluid dynamics, electromagnetism, quantum mechanics, etc.) are invoked to illustrate and elaborate upon the relevant mathematical techniques. The early chapters of the book introduce different types of functions, vectors and tensors, vector calculus, and matrices. In the subsequent chapters, more advanced topics like linear spaces, operator algebras, special functions, probability distributions, stochastic processes, analytic functions, Fourier series and integrals,Laplace transforms, Green's functions and integral equations are discussed. The book also features about 400 exercises and solved problems interspersed throughout the text at appropriate junctures, to facilitate the logical flow and to test the key concepts. Overall this book will be a valuable resource for a wide spectrum of students and instructors of mathematical physics.

Mathematics is an essential ingredient in the training of those seeking careers in science and engineering. No matter what the specialization, it is absolutely essential for scientists, physicists and engineers to not only develop an understanding of basic techniques of mathematics but also extend their manipulative skills to apply those techniques in their fields. The choice of mathematical topics in this book is evolved from the lectures given by the authors to undergraduate and postgraduate students in physics and engineering at IIT, New Delhi and at the National University of Singapore. Throughout the book, the authors have followed a style of presentation emphasising the derivation of techniques from the first principles. The illustrative material, solved examples and problems have been chosen for their value in applications of interest to scientists and engineers. This book should meet the requirements of students of engineering and physical sciences at the undergraduate and postgraduate levels. Large number of solved and unsolved numericals make the text also ideal for self-study.

This book is designed as an introduction to the mathematical concepts used to describe fundamental physics principles. Numerous examples and applications enable the reader to master complex mathematical concepts needed to define topics such as relativity, mechanics, and electromagnetics.Features:• Covers all of the mathematical concepts needed to study physics• Includes applications in every chapter • Instructor ancillaries for use as a textbook

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

The book covers a vast range of topics in applied mathematics. The book caters to the needs of a wide class of readers as all the topics have been discussed in detail and have been supported with exemplary problems for clear understanding of the subject by the students. A full chapter on'Ordinary Differential Equations in Physical Process'has been devoted to various problems from different corners of physical sciences. Stress has also been laid on'Numerical Methods'which help the students to develop a firm introductory base.

The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories.This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the'unreasonable effectiveness of mathematics'in modern physics.

This is a thorough treatment in one volume of the mathematical techniques vital in classical mechanics, electromagnetic theory, quantum theory, and relativity. Designed for junior, senior, and graduate courses in mathematical physics, it presents full explanations of function theory, vectors, matrices, dyadics, tensors, partial differential equations, and other advanced mathematical techniques in their logical order during the presentation of the various physical theories. The completeness of the derivations makes the book especially useful for self-study.Several topics seldom presented, such as electron theory and relativity, appear in considerable detail, because an understanding of them is increasingly vital to the student of atomic physics. But the author's treatment of his chosen subjects in classical physics is no way slighted, and his book has proved valuable to students in all fields of physics.The opening section provides scores of definitions, conversion factors, dimensional constants, and electromagnetic quantities for ready reference later on. There follows a full treatment of the main branches of classical physics: potential theory, spherical harmonics, vector analysis, dyadics, matrices, tensors, hydrodynamics, advanced dynamics, waves and vibrations, quantum mechanics, electromagnetic theory, and radiation theory. The book concludes with a discussion from first principles of the theory of relativity.Nearly 200 problems ranging over a wide level of difficulty and selected from many different fields of physics are included, with answers, at ends of chapters.'The treatment is more detailed than normal for an advanced text... excellent set of sections on Dyadics, Matrices, and Tensors.... The part on waves and vibrations is well done... problems well varied in difficulty.'― Journal of the Franklin Institute.

Title from PDF cover (viewed Feb. 10, 2010).

Description based on print version record.

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations. The book moves on to explain complex topics that often fall through the cracks in undergraduate programs, including the Dirac delta-function, multivalued complex functions using branch cuts, branch points and Riemann sheets, contravariant and covariant tensors, and an introduction to group theory. This expanded second edition contains a new appendix on the calculus of variation -- a valuable addition to the already superb collection of topics on offer. This is an ideal text for upper-level undergraduates in physics, applied physics, physical chemistry, biophysics, and all areas of engineering. It allows physics professors to prepare students for a wide range of employment in science and engineering and makes an excellent reference for scientists and engineers in industry. Worked out examples appear throughout the book and exercises follow every chapter. Solutions to the odd-numbered exercises are available for lecturers at www.wiley-vch.de/textbooks/.