Equations of Mathematical Physics and Special Functions (MAT0701)
Instructor: Chao Liu
Affiliation: Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology
Address: 1037 Luoyu Road, Wuhan, Hubei Province, China
Office: Math center 813, Enming Building
Email: chao_liu@hust.edu.cn
Lecture Notes
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Course Description
This course covers fundamental equations of mathematical physics, including Laplace’s equation, the wave equation, and the heat equation. It also explores special functions that commonly arise in these contexts. Videos and materials
Lecture Schedule and Notes
Week 1: Derivations of three types of equations and boundary conditions; Review of Fourier series.Week 1-1, Week 1-2
Week 2: Free vibration of a bounded string; Heat conduction in a finite rod.Week 2-1, Week 2-2
Week 3: Boundary value problems of the two-dimensional Laplace equation; Introduction to nonhomogeneous equations.Week 3-1, Week 3-2
Week 4: Methods for solving nonhomogeneous equations; Solving problems with nonhomogeneous boundary conditions; Introduction to eigenvalue problems.Week 4-1, Week 4-2
Week 5: D'Alembert’s formula and homogenization; The physical meaning of solutions to high-dimensional wave equation Cauchy problems.Week 5-1, Week 5-2
Week 6: Integral transform methods; Exercise session.Week 6-1, Week 6-2
Week 7: Green’s formula and applications; Green’s functions.Week 7-1, Week 7-2
Week 8: Applications of Green’s functions; Solutions to the Poisson equation.Week 8-1, Week 8-2