## 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