ジョージ.ブラウン・アルフケン

ハンス.J・ウェーバー

権平 健一郎

The revised fourth edition provides thorough coverage of the important mathematics needed for upper-division and graduate study in physics and engineering. After more than 28 years of successful class-testing, "Mathematical Methods for Physicists" is considered the standard text on the subject. Features a new chapter on nonlinear mathematical physics.

内容詳細

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises. Revised and updated version of the leading text in mathematical physics Focuses on problem-solving skills and active learning, offering numerous chapter problems Clearly identified definitions, theorems, and proofs promote clarity and understanding New to this edition: Improved modular chapters New up-to-date examples More intuitive explanations

Preface. Introduction. (1) Vector Analysis. (2) Vector Analysis In Curved Coordinates And Tensors. (3) Determines and Matrices. (4) Group Theory. (5) Infinite Series. (6) Functions of a Complex Variable I: Analytic Properties Mapping. (7) Functions of A Complex Variable II: Calculus of Residues. (8) Differntial Equations. (9) Sturm-Liouville Theory-Orthogonal Functions. (10) The Gamma Function (Factorial Function) (11) Bessel Functions. (12) Legendre Functions. (13) Special Functions. (14) Fourier Series. (15) Integral Transforms. (16) Intergal Equations. (17) Calculus of Variations. (18) Nonlinear Methods and Chaos. Appendix 1. Real Zeros of a Function. Appendix 2 Gaussian Quadrature General References Index * This revised Fourth Edition includes: * Modernized technology * Group theoretic methods brought together and expanded in a new chapter * An entirely new chapter on nonlinear mathematical physics * Significant revisions of the differential equations and complex variables chapters * Many new or improved exercises * Forty new or improved figures * An update of computational techniques for today's contemporary tools, such as microcomputers, Numerical Recipes, and Mathematica, among others.

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition. * Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition: * Updated content throughout, based on users' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell's equations* A new chapter on probability and statistics* More elementary sections have been deleted

連続・不連続を問わずあらゆる関数をサインとコサインで表現できるフーリエ級数。それを無限区間に拡張するフーリエ変換と微分方程式への応用。微分方程式が不能な問題にも威力を発揮する積分方程式。それに多くの物理原理を普遍的に表現するための変分法を解説し、最後に、いま急速に発展しつつある非線形の方法を展望する。

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