# SPRING 2006 COURSE ANNOUNCEMENT

## MATH 774: Topics in Scientific Computation

 Instructor: R. Cortez 410 Gibson Hall 862-3436 cortez@math.tulane.edu Lecture: TR 9:30-10:45am Gibson Hall 325 Office Hours: MT 11am-noon and by appointment

## matlab codes

### Course Description

This course will present a detailed analysis of the methods for numerically approximating the solution of ordinary and partial differential equations typically encountered in applications from engineering and physics. Mathematical theory, practical implementation and applications will be emphasized equally. Typical applications to be discussed include population dynamics, particle dynamics, waves, diffusion processes. By the end of the course, students will understand the mathematical and computational issues that must be considered when designing or choosing a numerical method for a particular application.

Prerequisites: Introductory knowledge of numerical analysis, ordinary and partial differential equations, or permission from the instructor. Some programming experience in Fortran, C, C++ or MATLAB will be helpful.

### Topics

Typical topics covered are: single and multi-step methods for ODE's, explicit and implicit methods, consistency, stability, systems of ODE's, linear advection PDE's, CFL condition, diffusion, dispersion, different boundary conditions, finite difference methods, integral equation methods, method of characteristics.

### Textbook

There will be no single textbook for this course. The material will be taken from several sources, including:

 J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations Chapman and Hall (1989).
 K. E. Atkinson, An Introduction to Numerical Analysis, Wiley (1978).
 J. D. Lambert, Computational methods in ordinary differential equations, Wiley (1973).
 R. LeVeque, Numerical methods for conservation laws, Birkhauser Verlag (1992).

The grade G will be computed numerically using the formula:
G = 0.5 H + 0.25 M + 0.25 F + 0.05 P
where H = homework, M = midterm, F = final project and P = participation (subjective points based on the student's class contributions and attendance).

### Exams

The midterm will be a 50-minute in-class exam. The final project will be assigned either individually or in groups of 2 and will require a written report and a presentation. Both parts will count toward the grade.

### Homework

Assignments will be given on Thursday and will be due the following Thursday unless otherwise specified. All assignments must be turned in at the beginning of the lecture on the day they are due.

### Important dates

 MLK holiday Mon. Jan. 16 Mardi Gras break Feb. 27 - Mar. 3 Midterm TBA Easter break Apr. 14 - 17 Last day of class Fri. Apr. 28 Finals period Apr. 29 - May 6