Mathematical Methods for Physics (1版)

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本書所包的內容十分豐富，幾乎包含應用數學所有的重要課題，如Complex Variables, Partial Differential Equations, Special Functions, Fourier Transforms, Laplace Transforms etc。就如同作者在序中所言，本書適合研究生或優秀大學部學生研習，本書有些難度。作者寫書的方式是在每章每節開始時，先討論一個課題的基本概念及方法，而後舉出很多各式各樣不同的例子，其中有許多是來自古典力學、流体力學、量子力學、電磁學的重要例子，如果讀者能將本書全部念完並消化之，將受益不淺 目次 Chapter 1.COMPLEX VARIABLES. Chapter 2.CONFORMAL MAPPINGS. Chapter 3.ELLIPTICAL FUNCTIONS. Chapter 4.TENSOR CALCULUS. Chapter 5.Sturm-Liouville Theory. Chapter 6.GAMMA FUNCTION. Chapter 7.BESSEL FUNCTION. Chapter 8.LEGENDRE FUNCTIONS. Chapter 9.OTHER SPECIAL FUNCTIONS Chapter 10.Fourier SeriesLAPLACE TRANSFORM. Chapter 11.LAPLACE TRANSFORM. Chapter 12.MELLIN AND HANKEL TRANSFORM.I Chapter 14.NTEGRAL EQUATIONS.

Mathematical Methods for Physics: An Introduction to Group Theory, Topology and Geometry

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This detailed yet accessible text provides an essential introduction to the advanced mathematical methods at the core of theoretical physics. The book steadily develops the key concepts required for an understanding of symmetry principles and topological structures, such as group theory, differentiable manifolds, Riemannian geometry, and Lie algebras. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering. The material has been subject to more than twenty years of feedback from students, ensuring that explanations and examples are lucid and considered, and numerous worked examples and exercises reinforce key concepts and further strengthen readers' understanding. This text unites a wide variety of important topics that are often scattered across different books, and provides a solid platform for more specialized study or research.

A Guided Tour of Mathematical Methods for the Physical Sciences (3版)

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Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.

ESSENTIAL MATHEMATICAL METHODS FOR THE PHYSICAL SCIENCES

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Essential Mathematical Methods for the Physical Sciences 作者：K. F. Riley, M. P. Hobson ISBN：9780521761147 版次：1 年份：2012 出版商：Cambridge University 頁數/規格：852頁/精裝單色 Description The mathematical methods that physical scientists need for solving substantial problems in their fields of study are set out clearly and simply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questions and homework problems. Each chapter concludes with a summary of the main procedures and results and all assumed prior knowledge is summarized in one of the appendices. Over 300 worked examples show how to use the techniques and around 100 self-test questions in the footnotes act as checkpoints to build student confidence. Nearly 400 end-of-chapter problems combine ideas from the chapter to reinforce the concepts. Hints and outline answers to the odd-numbered problems are given at the end of each chapter, with fully-worked solutions to these problems given in the accompanying Student Solutions Manual. Table of Contents 1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ordinary differential equations; 7. Series solutions of ordinary differential equations; 8. Eigenfunction methods for differential equations; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.