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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.