MATH 435-PARTIAL DIFFERENTIAL EQUATIONS-SPRING 2015

Text: Introduction to Partial Differential Equations, by Peter J. Olver (Springer-Verlag, 2013)

COURSE PLAN (tentative)

Ch. 2 Linear and Nonlinear Waves
2.2 uniform and non-uniform transport
2.4 wave equation on the line: d'Alembert's formula

Ch.3 Fourier Series
3.1, 3.2: Fourier series
3.3: differentiation and integration
3.5: convergence theorems

Ch.4 Separation of Variables
4.1: heat equation on an interval or circle
4.2: wave equation on an interval or circle

TEST 1

4.3: planar Laplace and Poisson equations

Ch. 6 Generalized Functions and Green's Functions

6.1: generalized functions
6.2: Green's functions in 1D
6.3: Green's function for the planar Poisson equation

TEST 2

Ch. 8 Linear and nonlinear evolution equations

8.1: fundamental solution to the heat equation
8.2: symmetry and simliarity
8.3: maximum principle
8.4: nonlinear diffusion


Ch. 11 Dynamics of planar media

TEST 3

Ch. 12 PDE in 3-dimensional space

FINAL