MATH 368K. Numerical Methods for Applications.

Unique #58355, Spring 2007
Solving scientific, engineering, and other problems often requires the use of numerical methods and computers. This course presents various basic numerical methods, discusses their mathematical properties, and provides practice in computer programming, as a continuation of M348.

Instructor:

Prof. Todd Arbogast
Office: RLM 11.162, Phone: 471-0166
E-Mail: arbogast@math.utexas.edu
Office hours: W 12:30-1:00 and Th 9:00-10:30 (or by appointment)

Textbook:

R. L. Burden and J. D. Faires, Numerical Analysis, 8th ed., 2005, Brooks/Cole Publishing (ISBN 0-534-39200-8).

Prerequisites:

M 348 with a grade of at least C.

Meeting:

11:00-12:00 MWF, RLM 5.120.

Course Description:

Introduction to the mathematical properties of numerical methods and their applications in computational science and engineering. We will study primarily chapters 7-12 of the text. A partial outline of these chapters follows.

7. Iterative techniques in matrix algebra
8. Approximation theory
9. Approximating eigenvalues
10. Numerical solution of nonlinear systems
11. Boundary-value problems for ODE's
12. Numerical solutions to PDE's

If time permits, we will cover Monte-Carlo techniques and minimization of multivariate functions.

Computer Accounts:

A computer account on the Mathematics Department network can be obtained in the Undergraduate Computer Lab, RLM 7.122.

Homework and Projects:

Homework and computer projects will be assigned periodically. It is acceptable for groups of students to help each other with the homework exercises and projects; however, each student must write up his or her own work.

Exams:

Two exams will be given during the semester. A comprehensive final exam will be given during finals week (Saturday, May 12, 7:00--10:00 p.m.).

Final Grade:

Grades on the two midterm exams will count 1/6 each in determining the final grade. For the homework and projects, the lowest score will be dropped, and the result will count 1/3 for the final grade. The final exam will count 1/3 for the final grade.