Math 591: Advanced Applied Mathematics

Course Description

Class meets Tuesdays 10:30 -- 11:50, Wednesdays 9:30-11 in DRL 4E9.

Office hours: Monday 4-5, Tuesday 12-1, or by appointment

The course will be an introductory graduate course on numerical analysis. We will cover rootfinding, numerical differentiation, numerical integration, numerical solution of ODEs, and numerical solution of PDEs.

We will not cover function approximation (for example, splines) because this would take away from time spent on PDEs. We will not cover numerical linear algebra, because that would be a semester course in its own right. We will not do stochastic ODEs or stochastic PDEs (applications to math finance, for example), because you need to learn how to do deterministic ODEs and PDEs before you go stochastic.

We will use matlab for all the computations. This is a very user-friendly package with a programming language similar to C. Sample programs will be provided to be modified and built upon. Not knowing how to program is not a reason not to take this course. Students who already know how to program are welcome to program in their preferred language.

Text: Atkinson's "An Introduction to Numerical Analysis"

Matlab Primer View the matlab primer using ghostview
Matlab Primer View the matlab primer using Adobe Acrobat
WARNING: Don't try to print the primer from acrobat, you'll get gibberish!

How to write up your homework.
On numerical integration.
On interpolation.
Diary from class on Wednesday 1/13
Homework due Wednesday 1/20.
Homework due Wednesday 1/27.
On cancellation errors and ill-conditioned problems: Trying to compute cos(x).
Homework due Wednesday 2/3.
On Finite-difference differentiation
On ODEs.
Homework due Thursday 2/11.
Homework due Thursday 2/18.
On Gaussian Elimination
On LU decompositions
Homework due Thursday 2/25.
On Iterative methods
Homework due Thursday 3/18.
On solving the heat equation using finite-difference methods and spectral methods.
How matlab does its fast Fourier transform.
On solving Burgers equation using spectral methods.
On solving the semilinear heat equation and the nonlinear Schroedinger equation using spectral methods.
On solving the KdV heat equation using an integrating factor method.
Diary from class 3/30/99.
Homework due on Tuesday 4/6.
Homework due on Wednesday 4/14.
Homework due on Monday 4/26.
On solving the advection equation.