Numerical Methods I (88-376)

This is a one-semester 90-minutes-a-week course to introduce computer science students to numerical methods. The main aims of the course are to expose the students to basic numerical methods that everyone should know, to develop an appreciation of the general issues to be considered in applying numerical methods (error analysis, order of approximation, conditioning etc.), and to introduce the software packages Matlab and Scilab. Mathematical theorems are stated, but the emphasis is more on the practical implications of the theorems than their proofs.

Review Class: Monday January 20, 18:00, 502/28.

You will need a postscript viewer (gv or ghostview) to view many of the links below

Dr. Yakov Krasnov is also teaching this course; see his web pages here.
2002/3 Information for Students
Matlab and Scilab links
Handouts/Links
- Introduction to Scilab
- Introduction to Matlab
- Error Analysis
  - A Simple Example
  - How to measure errors (in vectors and matrices) from the LAPACK users guide. Although it is all interesting, for our course we just need the first few screens, up to (and not including) the paragraph that starts "Here is some related notation we will use in our error bounds."
- Roots of Nonlinear Equations
  - Simple Matlab routine for Newton's method
  - Simple Scilab routine for Newton's method
  - Newton's method and Fractals pages by David Joyce, Clark University
- Numerical Linear Algebra
  - Conditioning (an example)
- Interpolation
  - Polynomial Interpolation: an example
  - Scilab/Matlab program for polynomial interpolation and some examples
  - Polynomial Interpolation Applet (by Ron Miech, UCLA)
  - Cubic splines: formulae and an example
  - A cubic spline applet (by Xing Cai, University of Oslo)
  - Another cubic spline applet (by Grady Wright, University of Colorado)
  - Don Lancaster's Guru's Lair Cubic Spline Library, a vast amount of interesting material.
- Approximation Theory
  - Common families of orthogonal polynomials
- Numerical Quadrature
- Integration of Ordinary Differential Equations
Exercise Sets
- Error Analysis
- Roots of Nonlinear Equations
- Numerical Linear Algebra
- Numerical Linear Algebra, continued
- Interpolation
- Approximation Theory
- Numerical Quadrature
- Integration of Ordinary Differential Equations
See also Ruthi Leabovich's site
Past Exams
The official syllabus.

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