MATH 774: Topics in Scientific Computation

Instructor: R. Cortez
410 Gibson Hall
     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.

Intended audience: Graduate students and advanced undergraduate students from mathematics, engineering and applied sciences.

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.


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.


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

[1] J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations Chapman and Hall (1989).
[2] K. E. Atkinson, An Introduction to Numerical Analysis, Wiley (1978).
[3] J. D. Lambert, Computational methods in ordinary differential equations, Wiley (1973).
[4] 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).


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.


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 holidayMon. Jan. 16
Mardi Gras breakFeb. 27 - Mar. 3
Easter breakApr. 14 - 17
Last day of classFri. Apr. 28
Finals periodApr. 29 - May 6