Page 14 - Excel for Scientists and Engineers: Numerical Methods

CONTENTS xi

Chapter 7 Integration 127
Area under a Curve ............................................................................................ 127
Calculating the Area under a Curve Defined by a Table of Data Points ..... 129
Calculating the Area under a Curve Defined by a Table of Data Points
by Means of a VBA Function Procedure .................................................. 130
Calculating the Area under a Curve Defined by a Formula ......................... 131
Area between Two Curves ........................................................................... 132
Integrating a Function ........................................................................................ 133
Integrating a Function Defined by a Worksheet Formula
by Means of a VBA Function Procedure .................................................. 133
Gaussian Quadrature .................................................................................... 137
Integration with an Upper or Lower Limit of Infinity ................................. 140
Distance Traveled Along a Curved Path ............................................................ 141
Problems ............................................................................................................. 143

Chapter 8 Roots of Equations 147
A Graphical Method .................................................................................... 147
The Interval-Halving or Bisection Method .................................................. 149
The Interval Method with Linear Interpolation
(the Regula Fulsi Method) ........................................................................ 151
The Regula Fulsi Method with Correction for Slow Convergence ............. 153
The Newton-Raphson Method ..................................................................... 154
Using Goal Seek ........................................................................................ 156
The Secant Method ...................................................................................... 160
The Newton-Raphson Method Using Circular Reference and Iteration ...... 161
A Newton-Raphson Custom Function ......................................................... 163
Bairstow's Method to Find All Roots of a Regular Polynomial .................. 166
Finding Values Other than Zeroes of a Function .............................................. 174
Using Goal Seek ... to Find the Point of Intersection of Two Curves ......... 174
Using the Newton-Raphson Method
to Find the Point of Intersection of Two Lines ......................................... 176
Using the Newton-Raphson Method to Find Multiple Intersections
of a Straight Line and a Curve .................................................................. 178
A Goal Seek Custom Function .................................................................... 180
Problems ............................................................................................................. 185

Chapter 9 Systems of Simultaneous Equations 189
Cramer's Rule ............................................................................................... 190
Solving Simultaneous Equations by Matrix Inversion ................................ 191
Solving Simultaneous Equations by Gaussian Elimination ......................... 191
The Gauss-Jordan Method ........................................................................... 196
Solving Linear Systems by Iteration .................................................................. 200
The Jacobi Method Implemented on a Worksheet ...................................... 200