Math 3171 Course Outline

MATH 3171 (Applied Mathematics) Course Outline

Week 1: introduction to partial differential equations; Fourier series; Week 2: Fourier series (cont.); eigenvalue problems; Week 3: Heat equation: the simplest case; heat equation: Dirichlet boundary conditions; Week 4: Heat equation: Neumann boundary conditions; heat equation: general cases; Week 5: Heat equation: general cases; Heat equation: higher dimension; Week 6: Review for Test 1; Test 1; Week 7: Wave equation: the simplest case; Wave equation: with source term; Week 8: Wave equation: with damping effects; Wave equation: Cauchy problem; Week 9: Wave equation: Cauchy problem on a half line; Wave equation: higher dimension; Week 10: Laplace equation in a rectangle: Dirichlet and Neumann boundary conditions; Week 11: Poisson equation in a rectangle; Laplace and Poisson equation in a disk; Week 12: Review for Test 2; Test 2; Week 13: Heat equation revisited: Weak Maximum principle and uniqueness of the solution Week 14: Wave equation revisited: continuous dependence of initial data; Laplace equation revisited: Maximum principle and uniqueness of the solution Week 15: Introduction to numerical methods of PDEs Week 16: Review for Final