Computer Sciences 323E

Elements of Scientific Computing

Instructor: A. K. Cline

Time: T - Th 9:30-11

Place: WRW 113

Unique Number: 52010

Prerequisite: C S 303E, M 408C, 408D, and 340L with a grade of at least C in each or permission of instructor.

Grading: Homework 30%, Midterm Exam 30%, Final Exam 40%

Textbook: Gerald Recktenwald: Numerical Methods with Matlab: Implementation and Application, Prentice Hall. (Optionally students should consider obtaining: The Student Edition of MATLAB)

Office: 3.104A Taylor Hall

Email: cline@cs.utexas.edu

Office Hours: Th 11-12, F 11-12, and by appointment

Teaching Assistant: Aniket Murarka

Email: aniket@mail.utexas.edu

Office Hours: To be announced

Course Outline:

1. Introduction to scientific computing

2. Basics of MATLAB

3. Floating point number systems

· Errors in representation and arithmetic

· Cancellation error

4. Interpolation

· General, linear and nonlinear

· Spline

5. Integration

· Polynomial based rules

· Composite rules

· Automatic and adaptive quadrature

· Extrapolation

6. Linear systems of equations

· Gaussian elimination

· Matrix condition

7. Nonlinear equations and Optimization

· Root finding

· Minimizing with one variable

· Minimizing with several variables

· Systems of non-linear equations

8. Initial Value Problems of ordinary differential equations

· Runge-Kutta methods

· Multistep methods