Math 320: Computer Methods in Mathematical Sciences I

Course Description

Prerequisites: Math 240 already taken or permission of instructor. While students do not need to already know how to program a computer, they should not be computer-phobic.

The students will write and run programs in matlab, which uses a programming language similar to C. Students will be taught rudimentary matlab and sample programs will be provided to be modified and built upon. The course covers: round-off error, root-finding, numerical integration, numerical differentiation, numerical linear algebra, and numerical solutions of ODEs (both initial value problems and boundary value problems). Theoretical and computational aspects of the methods will be discussed along with error analysis and a critical comparison of methods (accuracy and stability).

Class meets TuTh, 9:00 -- 10:20.

Matlab Primer View the matlab primer

Homework assigned 9/4, due 9/11.
Homework assigned 9/9, due 9/18.
On the bisection method
Homework assigned 9/11, due 9/18.
On the Newton-Raphson method
Homework assigned 9/18, due 9/25.
On the Secant method
Homework assigned 9/25, due 10/2.
On interpolation
Homework assigned 9/30, due 10/9.
On finite-difference approximations of the first derivative.
Homework assigned 10/2, due 10/16.
On numerical integration.
Homework assigned 10/7, due 10/16.
Homework assigned 10/20, due 10/23.
On Gaussian elimination
Homework assigned 10/21, due 10/30.
Homework assigned 10/23, due 10/30.
On LU decompositions
Homework assigned 10/29, due 11/6.
On linear transformations and norms you've never seen before
Homework assigned 10/30, due 11/6.
Homework assigned 11/4, due 11/13.
Homework assigned 11/13, due 11/20.
On ordinary differential equations.
Homework assigned 11/18, due 12/2.
Homework assigned 11/20, due 12/2.
On systems of ordinary differential equations.
Homework assigned 12/4, due 12/11.
Take-home portion of final, due 12/15 at 10:30 am.