Computing for numerical methods using visual C++

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Title:

Personal Author:

Shaharuddin Salleh, 1956-

Publication Information:

Hoboken, N.J. : Wiley-Interscience, 2008

ISBN:

9780470127957

Subject Term:

Microsoft Visual C# .NET

Numerical analysis -- Data processing

Added Author:

Zomaya, Albert Y.

Sakhinah Abu Bakar

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... Perpustakaan Raja Zarith Sofiah	30000010147746	QA76.73.C154 S52 2008	Non Circulating UTM Special Collection Materials	1:BOOK_ARC	Searching... Unknown
Searching... PSZ JB	30000010163513	QA76.73.C154 S52 2008	Open Access Book	Book	Searching... Unknown
Searching... PSZ JB	N10129543	QA76.73.C154 S52 2008	Non Circulating UTM Special Collection Materials	Book - UTM Special Collection (Closed Access)	Searching... Unknown
Searching... PSZ KL	30000010163512	QA76.73.C154 S52 2008	Open Access Book	Book	Searching... Unknown

Summary

A visual, interdisciplinary approach to solving problems in numerical methods

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 visual-ization 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++.

Author Notes

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

Reviews 1

Choice Review

Salleh (Universiti Teknologi, Malaysia) and others offer a wonderful, practical treatment of how to realize numerical methods in software for simulation and visualization in this book. The choice of Microsoft Visual C++ allows use of the conveniences of the Windows platform (such as graphics libraries) for creating visualizations, and for having fine control over the data being manipulated. C++ tends to be a bit complex in its own right. Perhaps Visual Basic would appeal to more people at a lower level of programming sophistication. Nevertheless, the book has a rich set of examples and good coverage of numerical methods taught through the 400 (upper-undergraduate) level. As such, this is a work that can live with students of mathematics throughout their undergraduate educational progression from lower- to upper-division undergraduate courses. The clarity of the book is excellent. Includes programming exercises at the end of most of the 13 chapters and a detailed index. Summing Up: Highly recommended. Lower-division undergraduate through professional applied mathematics and computer science collections. F. H. Wild III University of Rhode Island

Preface	p. xiii
Codes for Download	p. xvii
1 Modeling and Simulation	p. 1
1.1 Numerical Approximation	p. 1
1.2 C++ for Numerical Modeling	p. 3
1.3 Mathematical Modeling	p. 4
1.4 Simulation and Its Visualization	p. 6
1.5 Numerical Methods	p. 7
1.6 Numerical Applications	p. 7
2 Fundamental Tools for Mathematical Computing	p. 13
2.1 C++ for High-Performance Computing	p. 13
2.2 Dynamic Memory Allocation	p. 14
2.3 Matrix Reduction Problems	p. 22
2.4 Matrix Algebra	p. 35
2.5 Algebra of Complex Numbers	p. 43
2.6 Number Sorting	p. 51
2.7 Summary	p. 54
Programming Challenges	p. 55
3 Numerical Interface Designs	p. 56
3.1 Microsoft Foundation Classes	p. 56
3.2 Graphics Device Interface	p. 57
3.3 Writing a Basic Windows Program	p. 60
3.4 Displaying Text and Graphics	p. 68
3.5 Events and Methods	p. 69
3.6 Standard Control Resources	p. 71
3.7 Menu and File I/O	p. 78
3.8 Keyboard Control	p. 87
3.9 MFC Compatibility with .Net	p. 92
3.10 Summary	p. 95
4 Curve Visualization	p. 96
4.1 Tools for Visualization	p. 96
4.2 MyParser	p. 96
4.3 Drawing Curves	p. 106
4.4 Generating Curves Using MyParser	p. 115
4.5 Summary	p. 126
Programming Challenges	p. 126
5 Systems of Linear Equations	p. 127
5.1 Introduction	p. 127
5.2 Existence of Solutions	p. 128
5.3 Gaussian Elimination Techniques	p. 131
5.4 LU Factorization Methods	p. 142
5.5 Iterative Techniques	p. 161
5.6 Visualizing the Solution: Code5	p. 172
5.7 Summary	p. 189
Numerical Exercises	p. 190
Programming Challenges	p. 192
6 Nonlinear Equations	p. 193
6.1 Introduction	p. 193
6.2 Existence of Solutions	p. 194
6.3 Bisection Method	p. 195
6.4 False Position Method	p. 198
6.5 Newton-Raphson Method	p. 201
6.6 Secant Method	p. 203
6.7 Fixed-Point Iteration Method	p. 206
6.8 Visual Solution: Code6	p. 208
6.9 Summary	p. 225
Numerical Exercises	p. 225
Programming Challenges	p. 226
7 Interpolation and Approximation	p. 227
7.1 Curve Fitting	p. 227
7.2 Lagrange Interpolation	p. 228
7.3 Newton Interpolations	p. 231
7.4 Cubic Spline	p. 239
7.5 Least-Squares Approximation	p. 244
7.6 Visual Solution: Code7	p. 249
7.7 Summary	p. 264
Numerical Exercises	p. 265
Programming Challenges	p. 265
8 Differentiation and Integration	p. 267
8.1 Introduction	p. 267
8.2 Numerical Differentiation	p. 268
8.3 Numerical Integration	p. 271
8.4 Visual Solution: Code8	p. 279
8.5 Summary	p. 286
Numerical Exercises	p. 286
Programming Challenges	p. 287
9 Eigenvalues and Eigenvectors	p. 288
9.1 Eigenvalues and Their Significance	p. 288
9.2 Exact Solution and Its Existence	p. 289
9.3 Power Method	p. 291
9.4 Shifted Power Method	p. 292
9.5 QR Method	p. 294
9.6 Visual Solution: Code9	p. 302
9.7 Summary	p. 322
Numerical Exercises	p. 322
Programming Challenges	p. 323
10 Ordinary Differential Equations	p. 324
10.1 Introduction	p. 324
10.2 Initial-Value Problem for First-Order ODE	p. 325
10.3 Taylor Series Method	p. 327
10.4 Runge-Kutta of Order 2 Method	p. 330
10.5 Runge-Kutta of Order 4 Method	p. 333
10.6 Predictor-Corrector Multistep Method	p. 335
10.7 System of First-Order ODEs	p. 338
10.8 Second-Order ODE	p. 341
10.9 Initial-Value Problem for Second-Order ODE	p. 342
10.10 Finite-Difference Method for Second-Order ODE	p. 345
10.11 Differentiated Boundary Conditions	p. 351
10.12 Visual Solution: Code10	p. 358
10.13 Summary	p. 378
Numerical Exercises	p. 378
Programming Challenges	p. 380
11 Partial Differential Equations	p. 381
11.1 Introduction	p. 381
11.2 Poisson Equation	p. 385
11.3 Laplace Equation	p. 394
11.4 Heat Equation	p. 397
11.5 Wave Equation	p. 406
11.6 Visual Solution: Code11	p. 411
11.7 Summary	p. 437
Numerical Exercises	p. 437
Programming Exercises	p. 438
Index	p. 441

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Summary

Author Notes

Reviews 1

Choice Review

Table of Contents