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Numerical Methods with VBA Programming

Author(s): James Hiestand, PhD, The University of Tennessee at Chattanooga
  • ISBN-13: 9780763749644
  • ISBN-10:0763749648
  • Paperback    304 pages      © 2009
Price: $169.95 US List
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Numerical Methods with VBA Programming provides a unique and unified treatment of numerical methods and VBA computer programming, topics that naturally support one another within the study of engineering and science. This engaging text incorporates real-world scenarios to motivate technical material, helping students understand and retain difficult and key concepts. Such examples include comparing a two-point boundary value problem to determining when you should leave for the airport to catch a scheduled flight.

Numerical examples are accompanied by closed-form solutions to demonstrate their correctness. Within the programming sections, tips are included that go beyond language basics to make programming more accessible for students. A unique section suggest ways in which the starting values for non-linear equations may be estimated. Flow charts for many of the numerical techniques discussed provide general guidance to students without revealing all of the details. Useful appendices provide summaries of Excel and VBA commands, Excel functions accessible in VBA, basics of differentiation, and more! 

Features & Benefits

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!

Applicable Courses

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

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 4th 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


James Hiestand, PhD-The University of Tennessee at Chattanooga

Dr. Hiestand has 25 years of teaching experience preceded by 12 years in industry. He has taught numerous courses in numerical methods, thermal sciences, and basic mechanics. His work experience includes heat transfer and fluid flow modeling. He has authored several papers in these areas and coauthored others in nanoreactor modeling. In addition he has served as a consultant on heat transfer and fluid flow.

The following instructor resources are available to qualified instructors for download

ISBN-13: 9780763749644

Answers to In-Text Questions
Slides in PowerPoint Format

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