**
Math 33, Spring 2006, **

Mathematics in the Sciences and Engineering
##
Covered topics

- 1.
** Distributions and ODE's **

- Distributions, convolutions and fundamental solutions
- Laplace transform
- Fourier transform

- 2.
** PDE and mathematical models **

- 3.
**PDE on unbounded domains **

- The Heat equation
- The Wave Equation
- Well-posed problems
- An ill-posed problem: The Laplace Equation
- Semi-infinite domains
- Inhomogeneous equations and Duhamel's principle

- 4.
** PDE on bounded domains **

- Fourier and orthogonal expansions
- Sturm-Liouville problems
- Seperation of variables
- The Heat equation
- The Laplace equation
- Parameter identification
- Finite difference methods

As time permits

- 5.
** PDE in the life sciences**