Learn the fundamental concepts and methods of Mathematical Physics Equations in this comprehensive course from Beijing University of Chemical Technology. Master key topics including one-dimensional wave equations, heat conduction equations, and potential equations along with their boundary value problems. Explore the well-posedness and classification of mathematical physics equations, general solutions of linear partial differential equations, and traveling wave methods. Study separation of variables techniques for solving various boundary value problems, understand Legendre polynomials and their applications, and delve into integral transformations including Fourier and Laplace transforms. Apply these mathematical tools to solve real-world physics problems through practical examples and exercises, culminating in a final examination that tests your understanding of these advanced mathematical concepts.
Overview
Syllabus
- 课程简介及预备知识
- 第一章 数学物理方程及其定解问题
- 1.1 一维波动方程及其定解问题
- 1.2 热传导方程及其定解问题
- 1.3 位势方程及其定解问题
- 1.4 数理方程的适定性及分类
- 第二章 线性偏微分方程的通解
- 2.1 线性偏微分方程的通解
- 第三章 行波法
- 3.1 行波法
- 第四章 分离变量法
- 4.1 分离变量法求解一维波动方程的定解问题
- 4.2 分离变量法求解一维热传导方程的定解问题
- 4.3 分离变量法求解拉普拉斯方程的定解问题
- 第五章 勒让德多项式及其应用
- 5.1 勒让德多项式及其应用
- 第六章 积分变换
- 6.1 积分变换:傅里叶变换
- 6.2 积分变换:拉普拉斯变换
- 6.3 积分变换法的应用
- 期末考试
Taught by
XU LAN XI