Introductory Numerical Methods
Incorporating MATLAB

by Dr. Jerome Hahn
Bradley University
 

Contents


Chapter 1. Matrix Algebra and MATLAB.................................................
  1.1 Introduction..................................................... 1
  1.2 Matrix Algebra................................................ 4
  1.3 MATLAB Management................................... 10
  1.4 Problems......................................................... 11
1
Chapter 2. Computer Numbers and MATLAB..........................................
  2.1 Introduction....................................................  13
  2.2 Binary Numbers.............................................. 13
  2.3 Computer Representation................................ 16
  2.4 Problems......................................................... 19
13
Chapter 3. Taylor Approximation and M-files.........................................
  3.1 Introduction..................................................... 21
  3.2 Function M-files.............................................. 24
  3.3 Graphing and Symbolic Taylor Polynomials...... 26
  3.4 Problems......................................................... 29
21
Chapter 4. The Roots of f (x)....................................................................
  4.1 Introduction..................................................... 31
  4.2 The Bisection Method...................................... 32
  4.3 Newton's Method............................................ 35
  4.4 MATLAB Methods......................................... 40
  4.5 Root Finding Difficulties................................... 42
  4.6 Problems......................................................... 46
31
Chapter 5. Linear Algebraic Systems......................................................
  5.1 Introduction..................................................... 49
  5.2 Gaussian Elimination........................................ 50
  5.3 Matrix Factorization......................................... 55
  5.4 Tridiagonal Systems......................................... 60
  5.5 Iterative Methods............................................ 62
  5.6 Error in Linear Systems.................................... 67
  5.7 Problems......................................................... 68
49
Chapter 6. Polynomial Interpolation and Splines.....................................
  6.1 Introduction..................................................... 72
  6.2 Lagrange Interpolating Polynomials.................. 73
  6.3 Newton Interpolating Polynomials.................... 77
  6.4 Polynomial Interpolation - MATLAB............... 80
  6.5 Error in Polynomial Interpolation...................... 82
  6.6 Piecewise Interpolating Polynomials................. 84
  6.7 Interpolating Splines......................................... 85
  6.8 MATLAB and Splines..................................... 90
  6.9 Inverse Interpolation........................................ 93
  6.10 Problems....................................................... 94
72
Chapter 7. Least Squares and Data Models...........................................
  7.1 Introduction................................................... 98
  7.2 The Least Squares Method............................ 99
  7.3 Least Squares Polynomials and MATLAB..... 100
  7.4 Nonpolynomial Least Squares........................ 103
  7.5 Nonlinear Models.......................................... 105
  7.6 Problems....................................................... 110
98
Chapter 8. Numerical Differentiation and Integration............................
  8.1 Introduction................................................... 112
  8.2 Derivatives and Numerical Approximations.... 113
  8.3 Numerical Integration - Introduction............... 121
  8.4 The Trapezoidal Rule..................................... 122
  8.5 Simpson's Rule.............................................. 125
  8.6 Open Quadrature Rules................................. 128
  8.7 Error Analysis ............................................... 129
  8.8 Adaptive Quadrature and MATLAB.............. 134
  8.9 Gaussian Quadrature..................................... 139
  8.10 Integration of Numerical Data...................... 141
  8.11 Problems..................................................... 143
112
Chapter 9. Differential Equations.............................................................
  9.1 Introduction................................................... 147
  9.2 Euler's Method.............................................. 148
  9.3 The Improved Euler Method.......................... 152
  9.4 Higher Order One-Step Methods.................. 156
  9.5 Runge-Kutta Methods................................... 157
  9.6 Initial Value Problems and MATLAB............. 161
  9.7 Problems....................................................... 162
147
Answers....................................................................................................... 165
References................................................................................................... 173
Index........................................................................................................... 174

MATLAB is a registered trademark of The MathWorks, Inc.
Copyright © 2002 by Jerome Hahn, All rights reserved