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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.