Study Guide for Mathematical and Physical Methods

Author: Guo Yucai
Publisher:
Publish Date: 2006-02-01
Features: This book serves as a study guide for graduate and undergraduate engineering students taking the course "Mathematical Methods in Physics," and can also be used as a reference for teachers and researchers. The book is divided into 10 chapters, covering the following content: preliminary field theory, derivation of typical equations and formulation of boundary conditions, separation of variables in Cartesian coordinates and separation of variables for the two-dimensional Laplace equation in polar coordinates, series solutions of second-order linear ordinary differential equations and Sturm-Liouville eigenvalue problems, separation of variables in orthogonal curvilinear coordinates—introduction, properties, and applications of Bessel functions and Legendre polynomials, traveling wave method, integral transform method, Green's function method, and variational method for solving boundary value problems, as well as methods for solving simple integral equations and elementary solutions for certain nonlinear partial differential equations. Except for Chapter 10, each chapter is divided into three parts: 1) Basic requirements and content summary; 2) Basic training, including example analysis, exercises, solutions, and hints; 3) Expansion and improvement, including example analysis, exercises, solutions, and hints. Chapter 10 introduces methods for solving integral equations and certain nonlinear partial differential equations, primarily guiding readers to delve deeper into mathematical physics problems or broadening their perspectives.