MATH 368K: Numerical Methods for Applications

Solving scientific, engineering, and other problems often requires the use of numerical methods and computers. This course is a continuation of M348; it presents various basic numerical methods, discusses their mathematical properties, and provides practice in computer programming.

Administrivia:

Unique #59080, Spring 2008
Class home page: http://www.ices.utexas.edu/~organism/m368k/

Instructor:

Dr. James Rath
Office1: ACE 5.340, Phone: 232-7762
Office2: RLM 13.140, Phone: 232-6185
E-Mail: o r g a n i s m at math dot utexas dot edu
Office hours: Wed 1--3 (or by appointment or just stop by ACES)

Textbook:

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

The seventh edition of this book is on reserve in the PMA library. Used copies abound for sale on the web; ask me for suggestions if you're not sure where to look.

Prerequisites:

M348 with a grade of at least C. Also, CS303E or CS307 or their equivalent. And don't forget to bone up on your linear algebra (M341 or M340L) and your differential equations (M427K).

Meeting:

11:00--12:00 MWF in RLM 6.118.

Course Description:

Introduction to the mathematical properties of numerical methods and their applications in computational science and engineering. We will study 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

Time permitting, we will cover Monte-Carlo techniques and quasirandom integration, minimization of multivariate functions, Fourier transforms and wavelets (and their "fast" implementation), fast multipole methods, the Radon transform and imaging, or other topics of interest to the class.

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 their own work.

Exams:

Two exams will be given during the semester. A comprehensive final exam will be given during finals week (Thursday, May 8th, 2:00--5:00 PM).

Course Grade:

Grades on the two midterm exams and the final exam will each carry a 1/6th weight in determining the final grade. The homework and projects will carry the remaining weight. For the homework and projects, the lowest score will be dropped.