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