CIS 541 - Elementary Numerical Methods

Syllabus

Instructor: Prof. Roger Crawfis
Office: 683 Dreese Labs
Telephone: 292-2566
e-mail: crawfis [at] cse [dot] ohio-state [dot] edu
Course URL: http://www.cse.ohio-state.edu/~crawfis/cse541/index.html
Course Newsgroup: cse.course.cse541
Newsgroup Server: news.cse.ohio-state.edu

Course Summary

Survey of basic numerical methods including: number systems and errors of finite representation; solution of a single nonlinear equation; interpolation; numerical differentiation and integration; solution of linear systems, random numbers and Monte-Carlo methods, smooth function approximation and interpolation using splines.

Objectives

Students will gain insight into methods for computing approximate solutions to mathematical problems that occur frequently in computer simulations and real world problems. Particularly:

• Familiarity with finite number systems in computer arithmetic.
• Familiarity with fixed vs. variable precision.
• Familiarity with elementary numerical methods, for finding zeros of real functions, computing derivatives, computing definite integrals, solving linear systems, and interpolating data.

Text

Ward Cheney and David Kincaid, Numerical Mathematics and Computing, Fifth Edition, Brooks/Cole Publishing, 2004. Please see the Errata web page off of this link.

Course Notes will be available at the Tuttle Uniprint store. You can also order them on-line for easier pick-up later this week.

Topics

1. Introduction:
2. Taylor's series, Chapter 1
3. Background: computer arithmetic; rounding errors, machine precision, machine representation, Chapter 2
4. Root finding, Chapter 3.
5. Polynomial Interpolation, Chapter 4
6. Differentiation, Chapter 4
7. Integration, Chapters 5 and 6
8. Pseudo-random numbers and Monte Carlo Integration, Chapter 13
9. Systems of linear equations, Chapters 7 and 8