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.
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.
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:
- [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).
Grades
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 |