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Numerical Methods in Engineering

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Computer Science, and Mathematics. EE 4V95 (3 credits) Fall 2006. TR 9:30am-10:45am ... Prerequisites: Differential Equations (MATH2420); Applied Linear Algebra ... – PowerPoint PPT presentation

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Title: 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

3
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)

5
Example (continued)
  • Suppose the equations come from inexact
    measurements e.g.,
  • 34x 55y 89
  • 55y 89y 144 error
  • MATLAB
  • solve(34x55y89,55x89y144error)

6
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?

7
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

8
Summary
  • Dont believe everything (anything) the computer
    tells you!
  • Study Numerical Methods!!

9
Unexpected Results
  • Recall the sinc function

but
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