Numerical Methods in Engineering

1
Numerical Methods in Engineering

• Dr. William J. Pervin
• Professor of Electrical Engineering,
• Computer Science, and Mathematics

EE 4V95 (3 credits) Fall 2006 TR 930am-1045am
2
Introduction

• Textbook Numerical Methods Algorithms and
  Applications by Laurene V. Fausett. Pearson
  (Prentice-Hall) 2003 ISBN 0-13-031400-5
• Prerequisites Differential Equations (MATH2420)
  Applied Linear Algebra (EE2300) Programming in
  C/C/Java
• Software MATLAB and other packages

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Agenda

• (a) roots of equations in one variable
• (b) simultaneous linear equations
• (c) matrix analysis including LU factorization
  and eigenvalue determination
• (d) differentiation and integration of functions
  
• (e) ordinary and partial differential equations

4
Example

• Consider the two equations
• 34x 55y 89
• 55x 89y 144
• MATLAB
• solve(34x55y89,55x89y144)

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Example (continued)

• Suppose the equations come from inexact
  measurements e.g.,
• 34x 55y 89
• 55y 89y 144 error
• MATLAB
• solve(34x55y89,55x89y144error)

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Example (continued again)

• Try ( x , y ) (1.01 , 0.99)
• Try ( x , y ) (2.0 , 0.3819)
• Which is the better approximation to the correct
  answer?

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2nd Example

• Hilbert matrix hilb(4) in MATLAB
• 1 1/2 1/3 1/4
• 1/2 1/3 1/4 1/5
• 1/3 1/4 1/5 1/6
• 1/4 1/5 1/6 1/7
• MATLAB
• H1 1/2 1/3 1/4 1/2 1/3 1/4 1/5 1/3 1/4 1/5
  1/6 1/4 1/5 1/6 1/7

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Summary

• Dont believe everything (anything) the computer
  tells you!
• Study Numerical Methods!!

9
Unexpected Results

• Recall the sinc function

but
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