Instructor: Donald Allison, e-mail allison@cs.vt.edu

Office: 626 McBryde, tel. no. 231 - 4212

Office Hours: MWF 2.30 - 4.00 pm

Class meets: GBJ 102 MW 11.00 - 11.50 pm; Labs held in McB 126

Index 1398 @ M 3.00 pm, Index 1399@ W 4.00 pm

GTA: Jeremy Rotter, e-mail jrotter@vt.edu

Office: 116 McBryde Hall

Office Hours: 10-1, Thursdays

This course is intended as an introduction to techniques for carrying out numerical computation on computers, historically one of the fundamental disciplines of computer science. It may be considered to be a preparatory course for a course in numerical analysis. While mathematical in nature, emphasis is given to programming techniques and style, and techniques for de-bugging malfunctioning numerical methods. Laboratory exercises will be carried out using the Mathematica system; experience with this package is not assumed.

Prerequisites: Math 2214, CS 1014 or equivalent.

Each programming question will be graded in the following way: answer,

60% ; numerical techniques 20% ; style 20%. Assignments are due at the beginning of class on the due date. Late work may be penalized up to 15% per day late.

The Honor Code will apply to all assignments. The programs or problem solutions must be the work of the individual student.

Text: Elementary Numerical Computing with Mathematica, Skeel and Keiper, McGraw Hill, 1993.

1: Above all READ and UNDERSTAND notes on blackboard. Experience has shown that the single most important thing you can do to ensure success in this course is to come to class faithfully.

2: If any student needs special accommodations because of a disability please contact the instructor during the first week of classes.

0. Introduction to Numerical Computation

Mistakes, errors, rounding and truncation errors

1. Computer Arithmetic

Floating point numbers, range, precision, EPS

2. Linear Systems

Matrix formulation, sparse and stored matrices

Gaussian elimination, partial pivoting

Iterative methods, Gauss - Seidel method

Sparse matrix storage

3. Finite Differences

Taylor Series, tables, effect of errors

4. Interpolation

Definition of problem, difference formulae

Lagrange interpolation, cubic splines

5. Numerical Differentiation and Integration

Problems with differentiation

Trapezoidal and Simpson formulae

Interval halving, h2 extrapolation

Gaussian quadrature and related formulae

6. Root Finding

Bisection, secant, Newton methods and extensions

7. Linear Least Squares

Exploring data, normal equations, orthogonal transformations

8. Ordinary Differential Equations

Initial and boundary value problems

Euler and Runge-Kutta methods

Multi-step methods