Math 700: Fall 2000
Special Topics in Applied and Numerical Analysis:
Scientific Computing in C

Course information

Course:	Math 700/0101: Scientific Computing in C
Time/Place:	MW 4:00pm-5:15pm, SS 111
Instructor:	Dr. Rouben Rostamian
Office:	MP 417
Phone:	410-455-2458
Email:	rostamian@umbc.edu
Office hours:	MW 3:00-4:00 and by appointment

Course Description

This is a hands-on computational mathematics course with emphasis on programming in C. The goal is to quickly impart the necessary algorithmic and programming skills to enable the students to build moderate- to large-scale application programs and gain a mastery of the C programming language in the context of scientific computing.

Previous experience in programming is not required; a substantial part of the course will consists of introduction to C with special emphasis on common idioms used in scientific computing. Through the semester the students will gradually build their own computing library and will successively apply it to solve increasingly complex computational projects.

Prerequisites: Math 221 (linear algebra), Math 251 (multivariable calculus)

Syllabus

The Gauss-Jordan algorithm for solving an mxn linear system of equations
Haar wavelets applied to the processing and compression of grayscale and color images
Solving statically determinate 2D trusses via the statics equations of equilibrium
The Nelder-Mead downhill simplex algorithm for finding the minima of a function f : Rⁿ -> R
Solving statically indeterminate 2D trusses via minimizing energy
The Gauss quadrature method for numerical integration, with an algorithm to generate Legendre polynomials, quadrature points and weights on the fly
A generic Finite Element Solver for solving elliptic partial differential equations on irregular 2D domains with mixed Dirichlet and Neumann boundary conditions

Textbook

There is no textbook which covers the selection of topics planned for this course. I will provide plenty of reading material from various sources throughout the semester. Students are expected to take detailed notes.

Required reading: Kernighan and Ritchie, The C Programming Language

Grading method

I will collect and grade the weekly programming assignments. Your course grade will be based on your cumulative performance on these assignments.

Sample image filtered with Haar wavelets

The original 256x256 image was transformed via Haar wavelets. Then the least significant coefficients were dropped and the image was reconstructed with the remaining coefficients. The relative L² errors of truncation in the three reconstructed images are 2, 3, and 6 percent. The information from the original image retained are 10%, 5%, and 1%, respectively.

[vivian000.jpg]
Original image
...with 10% of the original information

...with 5% of the original information
...with 1% of the original information

The URL of this document is http://www.math.umbc.edu/~rouben/2000-09-math700/
This page created on May 10, 2000 -- it will be updated frequently throughout the semester
Author: rostamian@umbc.edu

Original image	...with 10% of the original information
...with 5% of the original information	...with 1% of the original information