Course Description
The basic partial differential equations of mathematical physics: Laplace's equation, the wave equation, and the heat equation. Separation of variables and Fourier series techniques are featured.
Additional Requirements for Graduate Students:
Extra probelms on weekly homework.
Athena Title
Intro to PDEs
Prerequisite
MATH 2700 and (MATH 2270 or MATH 2500 or MATH 3510 or MATH 3510H) and MATH 3100
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
This is a course in partial differential equations with emphasis on specific partial differential equations. Students will solve these equations by using separation of variables and fundamental convergence properties of analysis. By repeated application of these techniques, students will be able to solve other partial differential equations that occur in physical sciences. Students will also obtain a basic understanding of Fourier series, the Sturm-Liouville method, and some special functions.
Topical Outline
1. The basic framework: the key equations -- Laplace's equation (elliptic), heat equation (parabolic), wave equation (hyperbolic); Cauchy problem; Dirichlet and Neumann boundary problems 2. Techniques: Separation of variables, Sturm-Liouville method; Fourier series; method of characteristics, Green's functions 3. Detailed treatment of wave equation, Huygens' principle 4. Detailed treatment of heat equation, regularity, maximum principle 5. Detailed treatment of Laplace's equation, maximum principle
Syllabus