Numerical Methods with VBA Programming

Includes flow charts for many of the numerical techniques discussed for extra guidance.

Tips are also included throughout that go beyond language basics to make programming more accessible for the readers.

Includes examples accompanied by closed-form solutions.

Contains appendices with summaries of Excel and VBA commands, Excel functions accessible in VBA, basics of differentiation, and more!

Chapter 1  Introduction

     1.1  Why numerical methods?
     1.2  Why programming?
     1.3  Why numerical methods and programming?
      1.4  Why VBA?

Chapter 2   Programming basics: arithmetic, input/output, and all that 

     2.1  General remarks 
     2.2  Parts of a computer program
     2.3  Opening VBA
      2.4  VBA statements 
     2.5  Input/output 
     2.6  A simple program
     2.7  Documentation
     2.8  Running VBA
     2.9  Flowcharts
     2.10  Variable types
     2.11  Example: the real roots of a quadratic equation
     2.12  User-defined types - complex variable type
     2.13   Debugging
     2.14   File saving and security level
     2.15   A word of encouragement
      2.16   Exercises

Chapter 3  Errors, series, and uncertainty

      3.1  Types of errors
     3.2  Why series?
     3.3  The Taylor series
     3.4  Example:  the cosine function
     3.5  Maclaurin series
     3.6  An exponential example 
     3.7  Uncertainty
     3.8  Another example
      3.9  Exercises

Chapter 4  Decisions and loops: Which is bigger? How many times? 

     4.1  Why comparisons?
     4.2  If statements
     4.3  ElseIf
     4.4  Boolean operations
     4.5  Sine series program
     4.6  Conditional loops: the Do While loop
      4.7  Definite loops: the For loop
     4.8  Nested loops 
     4.9  Constant calculations and loops
     4.10  Exercises

Chapter 5  Numerical integration

      5.1  The basic idea: area
     5.2  The trapezoid rule
     5.3  Simpson's 1/3 rule, something for nothing
     5.4  Simpson's 3/8 rule
     5.5  Richardson extrapolation, a clever idea
     5.6  Romberg integration
     5.7  Integration of data
     5.8  The extended mid-point rule 
      5.9  Exercises

Chapter 6  Subprograms and functions: useful specialists

      6.1  Why subprograms and functions?
     6.2  Subprogram form
     6.3  Function form
     6.4  Example:  the trapezoid rule
     6.5  Unused arguments
     6.6  Excel functions in VBA
      6.7  Exercises

Chapter 7  Roots of non-linear equations: finding zero 

     7.1  What is a root?
     7.2  The Newton-Raphson method
     7.3  The secant rule
     7.4  Estimating starting values
     7.5  Two-equation Newton-Raphson
     7.6  General non-linear equation sets
     7.7  Multiple equations with the secant rule
     7.8  Flowchart: two equations with the secant rule
     7.9  The Excel solver
      7.10  Exercises

Chapter 8  Ordinary differential equations: take one step forward

      8.1  The basic idea
     8.2  Example: vehicle velocity
     8.3  Application of the Euler method
     8.4  Other Euler methods
     8.5  Second order equations
     8.6  The 4^th order Runge-Kutta method
     8.7  Another example with coupled equations
     8.8  Two-point boundary value problems
     8.9  A predictor-corrector method
     8.10 The Cash-Karp Runge-Kutta method 
     8.11  Stability
      8.12  Stiff differential equations
     8.13  Ordinary differential equation methods and numerical integration
     8.14  Program step control – trapping
      8.15  Exercises

Chapter 9  Sets of linear equations

      9.1  Lots of linear equations
     9.2  Gauss elimination with partial pivoting
     9.3  Gauss-Seidel iteration
     9.4  Comparison of Gauss elimination and Gauss-Seidel
     9.5  Matrix inverses
     9.6  Gauss-Jordan
     9.7  Over-determined sets of linear equations
     9.8  Excel inverses and linear equation solutions
      9.9  Exercises

Chapter 10  Arrays, variables with a family name

      10.1  One-dimensional arrays
     10.2  Example: grade averaging
     10.3  Dynamic dimensioning
     10.4  Example:  Sorting an array
      10.5  Multi-dimensional arrays  
     10.6  Gauss elimination flowchart
     10.7  Gauss-Seidel flowchart
     10.8  Gauss-Jordan flowchart
     10.9  Romberg integration flowchart
     10.10  Thomas algorithm flowchart
      10.11  Exercises

Chapter 11 Curve fitting 

     11.1  Introduction
     11.2  Linear interpolation
     11.3  Lagrange interpolating polynomials
     11.4  Linear regression1
     11.5  Polynomial regression
     11.6  The power law 

     11.7  The exponential fit
     11.8  Multiple regression
     11.9  Splines 
     11.10  Curve fitting with Excel
     11.11  Exercises 

Chapter 12  Elliptic partial differential equations
    
      12.1  Introduction
     12.2  Derivative forms
     12.3  An elliptic partial differential equation example
     12.4  Elliptic equation solver flowchart
     12.5  Solving elliptic partial differential equations with Excel
      12.6  Derivative boundary condition
     12.7  Exercises

Appendix 1  Excel Basics 

Appendix 2  Computer representation of numbers 

Appendix 3  Summary of VBA Commands 

Appendix  4  Glossary 

Appendix  5  Numerical methods with the Casio  fx115MS calculator 

Appendix 6  Excel functions available in VBA 

Appendix 7  Differentiation fundamentals 

Appendix 8  VBA program for Cash-Karp Runge-Kutta

Appropriate for courses within the departments of Engineering, Computer Science, Physics, and Chemistry.