Computing for Numerical Methods Using Visual C++
Published on 12. July 2008
516 pages
978-0-470-19262-7 (ISBN)
Description
A visual, interdisciplinary approach to solving problems innumerical methods
Computing for Numerical Methods Using Visual C++ fills the needfor a complete, authoritative book on the visual solutions toproblems in numerical methods using C++. In an age of boundlessresearch, there is a need for a programming language that cansuccessfully bridge the communication gap between a problem and itscomputing elements through the use of visual-ization for engineersand members of varying disciplines, such as biologists, medicaldoctors, mathematicians, economists, and politicians. This booktakes an interdisciplinary approach to the subject and demonstrateshow solving problems in numerical methods using C++ is dominant andpractical for implementation due to its flexible language format,object-oriented methodology, and support for high numericalprecisions.
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, givingreaders free access to all of the codes discussed in the book aswell as an equation parser called "MyParser" that can be used todevelop various numerical applications on Windows. Computing forNumerical Methods Using Visual C++ serves as an excellent referencefor students in upper undergraduate- and graduate-level courses inengineering, science, and mathematics. It is also an ideal resourcefor practitioners using Microsoft Visual C++.
Reviews / Votes
"The clarity of the book is excellent." (CHOICE, May 2008)More details
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Shaharuddin Salleh | Albert Y. Zomaya | Sakhinah A. Bakar
Computing for Numerical Methods Using Visual C++
Book
01/2008
Wiley
€162.50
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Shaharuddin Salleh | Albert Y. Zomaya | Sakhinah A. Bakar
Computing for Numerical Methods Using Visual C++
Software
05/2007
Wiley
€156.87
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Persons
Shaharuddin Salleh, PhD, is Professor in ComputationalMathematics, Faculty of Science (Mathematics), UniversitiTeknologi, Malaysia (UTM). Dr. Salleh's research is in parallelcomputing algorithms and scheduling, mobile computing, intelligentsystems, and numerical/combinatorial optimization problems. He isalso an IT Manager at the Research Management Centre, UTM.
Albert Y. Zomaya, PhD, is the Head of School and CISCO SystemsChair Professor of Internetworking in the School of InformationTechnologies at the University of Sydney. He is the author orcoauthor of several books and more than 300 publications. He is anIEEE Fellow.
Sakhinah Abu Bakar is Lecturer in Computational Mathematics atthe School of Mathematical Sciences, Faculty of Science andTechnology, National University of Malaysia. She is currentlypursuing her PhD degree at the University of Sydney.
Content
Chapter 1: Overview of C++.
Language style and organization.
Data types, variables.
Loops and branches.
Array, pointer, function, structure.
Classes and objects.
Inheritance, polymorphism, encapsulation.
Complexity analysis.
Chapter 2: Visual C++ Methods.
MFC library .
Fundamental interface tools.
Text displays.
Graphics and images.
Writing the first program.
Chapter 3: Fundamental Mathematical Tools.
C++ for High-Performance Computing.
Dynamic memory allocation.
Allocation for one-dimensional arrays.
Allocation for higher-dimensional arrays.
Case Study: Matrix multiplication problem.
Matrix elimination problems.
Vector and matrix norms.
Row operations.
Matrix reduction to triangular form.
Computing the determinant of a matrix.
Computing the inverse of a matrix.
Matrix algebra.
Data passing between functions.
Matrix addition and subtraction.
Matrix multiplication.
Matrix inverse.
Putting the pieces together.
Algebra of complex numbers.
Addition and subtraction.
Multiplication.
Conjugate.
Division.
Inverse of a complex number.
Putting the pieces together.
Number Sorting.
Programming Exercises.
Chapter 4: System of Linear Equations.
Systems of Linear Systems.
Existence of Solutions.
Elimination Techniques.
Gauss Elimination Method.
Gauss Elimination with Partial Pivoting.
Gauss-Jordan Method.
LU Factorization Techniques.
Crout Method.
Doolittle Method.
Cholesky Method.
Thomas Algorithm.
Iterative Techniques.
Jacobi Method.
Gauss-Seidel Method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 5: Nonlinear Equations.
Iterative methods: convergence, stability.
Background: existence of solution, MVT, errors, etc..
Bisection method.
False-point position method.
Newton method.
Secant method.
Fixed-point iterative method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 6: Interpolation and Approximation.
Concepts, existence, stability.
Lagrange.
Newton methods: forward, backward.
Stirling method.
Cubic spline interpolation.
Least-square approximation.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 7: Differentiation and Integration.
Taylor series.
Newton methods (forward, backward, central).
Trapezium method.
Simpson method.
Simpson 3/8 method.
Gauss quadrature.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 8: Eigenvalues and Eigenvectors.
Characteristic polynomials.
Power method.
Power method with shifting.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 9: Ordinary Differential Equations.
Existence, uniqueness, stability, convergence.
IVP: Taylor method.
Euler method.
Runge-Kutta of order 2 method.
Runge-Kutta of order 4 method.
Higher dimensional orders.
Multistep methods: Adams-Bashforth method.
Boundary Value Problems: finite-difference method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 10: Partial Differential Equations.
Existence, uniqueness, stability, convergence.
Elliptic problem: Laplace equation.
Elliptic problem: Poisson equation.
Parabolic problem: heat equation.
Hyperbolic problem: wave equation.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
Chapter 11: Finite Element Methods.
One-dimensional heat problem.
Linear approximation.
Quadratic approximation.
Two-dimensional problem: triangulation method.
Visual C++ Solution Interface.
Summary.
Programming Exercises.
