Computing for Numerical Methods Using Visual C++ / Edition 1

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Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++. In an age of boundless research, there is a need for a programming language that can successfully bridge the communication gap between a problem and its computing elements through the use of visualization for engineers and members of varying disciplines, such as biologists, medical doctors, mathematicians, economists, and politicians. This book takes an interdisciplinary approach to the subject and demonstrates how solving problems in numerical methods using C++ is dominant and practical for implementation due to its flexible language format, object-oriented methodology, and support for high numerical precisions.

In an accessible, easy-to-follow style, the authors cover: Numerical modeling using C++, Fundamental mathematical tools, MFC interfaces, Curve visualization, Systems of linear equations, Nonlinear equations, Interpolation and approximation, Differentiation and integration, Eigenvalues and Eigenvectors, Ordinary differential equations, Partial differential equations.

This reader-friendly book includes a companion Web site, giving readers free access to all of the codes discussed in the book as well as an equation parser called "MyParser" that can be used to develop various numerical applications on Windows. Computing for Numerical Methods Using Visual C++ serves as an excellent reference for students in upper undergraduate- and graduate-level courses in engineering, science, and mathematics. It is also an ideal resource for practitioners using Microsoft Visual C++.

About theAuthor:
Shaharuddin Salleh, PhD, is Professor in Computational Mathematics, Faculty of Science (Mathematics), Universiti Teknologi, Malaysia (UTM)

About the Author:
Albert Y. Zomaya, PhD, is the Head of School and CISCO Systems Chair Professor of Internetworking in the School of Information Technologies at the University of Sydney

About the Author:
Sakhinah Abu Bakar is Lecturer in Computational Mathematics at the School of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia

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Editorial Reviews

From the Publisher
"The clarity of the book is excellent." (CHOICE, May 2008)
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Product Details

  • ISBN-13: 9780470127957
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 12/4/2007
  • Edition number: 1
  • Pages: 448
  • Product dimensions: 6.40 (w) x 9.41 (h) x 1.09 (d)

Meet the Author

Shaharuddin Salleh, PhD, is Professor in Computational Mathematics, Faculty of Science (Mathematics), Universiti Teknologi, Malaysia (UTM). Dr. Salleh's research is in parallel computing algorithms and scheduling, mobile computing, intelligent systems, and numerical/combinatorial optimization problems. He is also an IT Manager at the Research Management Centre, UTM.

Albert Y. Zomaya, PhD, is the Head of School and CISCO Systems Chair Professor of Internetworking in the School of Information Technologies at the University of Sydney. He is the author or coauthor of several books and more than 300 publications. He is an IEEE Fellow.

Sakhinah Abu Bakar is Lecturer in Computational Mathematics at the School of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia. She is currently pursuing her PhD degree at the University of Sydney.

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Table of Contents

Preface     xiii
Codes for Download     xvii
Modeling and Simulation     1
Numerical Approximation     1
C++ for Numerical Modeling     3
Mathematical Modeling     4
Simulation and Its Visualization     6
Numerical Methods     7
Numerical Applications     7
Fundamental Tools for Mathematical Computing     13
C++ for High-Performance Computing     13
Dynamic Memory Allocation     14
Matrix Reduction Problems     22
Matrix Algebra     35
Algebra of Complex Numbers     43
Number Sorting     51
Summary     54
Programming Challenges     55
Numerical Interface Designs     56
Microsoft Foundation Classes     56
Graphics Device Interface     57
Writing a Basic Windows Program     60
Displaying Text and Graphics     68
Events and Methods     69
Standard Control Resources     71
Menu and File I/O     78
Keyboard Control     87
MFC Compatibility with .Net     92
Summary     95
Curve Visualization     96
Tools for Visualization     96
MyParser     96
Drawing Curves     106
Generating Curves Using MyParser     115
Summary     126
Programming Challenges     126
Systems of Linear Equations     127
Introduction     127
Existence of Solutions     128
Gaussian Elimination Techniques     131
LU Factorization Methods     142
Iterative Techniques     161
Visualizing the Solution: Code5     172
Summary     189
Numerical Exercises     190
Programming Challenges     192
Nonlinear Equations     193
Introduction     193
Existence of Solutions     194
Bisection Method     195
False Position Method     198
Newton-Raphson Method     201
Secant Method     203
Fixed-Point Iteration Method     206
Visual Solution: Code6     208
Summary     225
Numerical Exercises     225
Programming Challenges     226
Interpolation and Approximation     227
Curve Fitting      227
Lagrange Interpolation     228
Newton Interpolations     231
Cubic Spline     239
Least-Squares Approximation     244
Visual Solution: Code7     249
Summary     264
Numerical Exercises     265
Programming Challenges     265
Differentiation and Integration     267
Introduction     267
Numerical Differentiation     268
Numerical Integration     271
Visual Solution: Code8     279
Summary     286
Numerical Exercises     286
Programming Challenges     287
Eigenvalues and Eigenvectors     288
Eigenvalues and Their Significance     288
Exact Solution and Its Existence     289
Power Method     291
Shifted Power Method     292
QR Method     294
Visual Solution: Code9     302
Summary     322
Numerical Exercises     322
Programming Challenges     323
Ordinary Differential Equations     324
Introduction     324
Initial-Value Problem for First-Order ODE     325
Taylor Series Method      327
Runge-Kutta of Order 2 Method     330
Runge-Kutta of Order 4 Method     333
Predictor-Corrector Multistep Method     335
System of First-Order ODEs     338
Second-Order ODE     341
Initial-Value Problem for Second-Order ODE     342
Finite-Difference Method for Second-Order ODE     345
Differentiated Boundary Conditions     351
Visual Solution: Code10     358
Summary     378
Numerical Exercises     378
Programming Challenges     380
Partial Differential Equations     381
Introduction     381
Poisson Equation     385
Laplace Equation     394
Heat Equation     397
Wave Equation     406
Visual Solution: Code11     411
Summary     437
Numerical Exercises     437
Programming Exercises     438
Index     441
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