CIS 541: Elementary Numerical Methods

Description

Survey of basic numerical methods: number systems and errors of finite representation; solution of a single nonlinear equation;zeros of polynomials; interpolation; numerical integration; solution of linear systems.

Level, Credits, Class Time Distribution

UG 3 (three hour lectures)

Prerequisites

CIS 200 or 201 or 211 or En Graph 167, and Math 153

Quarters Offered

Au, Wi, Sp, Su

General Information, Exclusions, etc.

A pocket calculator will be required for in-class exercises and exams.
Computer Lab assignments will be carried out on campus workstations or on PC's using some suitable programming language.

Objectives

Familiarity with finite number systems in computer arithmetic
Familarity with fixed vs. variable precision, and floating-point vs. interval arithmetic
Familiarity with elementary numerical methods, as implemented in current software,
- for finding zeros of real functions, and real and complex zeros of polynomials,
- computing derivatives,
- computing definite integrals,
- solving linear syatems
Exposure to applications of mathematical software to real world problems.

Texts

Precise Numerical Methods Using C++, Oliver Aberth, Academic Press, 1998.

Relationship to ABET Criterion 3

Relationship to CSE Program Objectives

a	b	c	d	e	f	g	h	i	j	k
XXX	XX	XX		X				X		XX

1a	1b	1c	2a	2b	3a	3b	3c	4a	4b
XX	XXX	XX	XX					XX	XX

Topics

No. of Wks.	Topics
1	Introduction; mathematical software.
1	Number systems (integer, rational, algebraic, real, complex, interval); computer arithmetic; round-off errors; variable precisioninterval arithmetic
1	Solvable problems and non-solvable problems
1	Computing derivatives and integrals; computer algebra vs. recursive differential of code lists
1	Mid-term Review and Exam
2	Finding zeros of real functions; polynomial zeros
2	Problems of linear algebra
1	Applications; final review

Grading Plan

Lab Assignments	50%
Midterm Exam	20%
Final Exam	30%

Prepared By

R. Moore (Date: March 31, 1999).