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