| Titre : | Computing for Numerical Methods Using Visual C++ | | Type de document : | texte imprimé | | Auteurs : | Salleh Shaharuddin, Auteur ; Albert Y. Zomaya, Auteur ; Sakhinah Abu Bakar, Auteur | | Editeur : | USA : John wiley & Sons | | Année de publication : | 2008 | | Importance : | 448 p. | | Présentation : | couv. ill. en coul. | | Format : | 25 cm. | | ISBN/ISSN/EAN : | 978-0-470-12795-7 | | Langues : | Anglais (eng) | | Catégories : | INFORMATIQUE
| | Index. décimale : | 08-02 Logiciels et programmation | | Résumé : | 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++
| | Note de contenu : | Contents
1-Modeling and Simulation
1.1 Numerical Approximation
1.2 C++ for Numerical Modeling
1.3 Mathematical Modeling
1.4 Simulation and Its Visualization
1.5 Numerical Methods
1.6 Numerical Applications
2-Fundamental Tools for Mathematical Computing
2.1 C++ for High‐Performance Computing
2.2 Dynamic Memory Allocation
2.3 Matrix Reduction Problems
2.4 Matrix Algebra
2.5 Algebra of Complex Numbers
2.6 Number Sorting
Summary
Programming Challenges
3-Numerical Interface Designs
3.1 Microsoft Foundation Classes
3.2 Graphics Device Interface
3.4 Writing a Basic Windows Program
3.5 Displaying Text and Graphics
3.6 Events and Methods
3.7 Standard Control Resources
3.8 Menu and File I/O
3.9 Keyboard Control
3.10 MFC Compatibility with .Net
Summary
4-Curve Visualization
4.1 Tools for Visualization
4.2 MyParser
4.3 Drawing Curves
4.4 Generating Curves Using MyParser
4.5 Summary
4.6 Programming Challenges
5-Systems of Linear Equations
5.1 Introduction
5.2 Existence of Solutions
5.3 Gaussian Elimination Techniques
5.4 LU Factorization Methods
5.5 Iterative Techniques
5.6 Visualizing the Solution: Code5
5.7 Summary
5.8 Numerical Exercises
5.9 Programming Challenges
6-Nonlinear Equations
6.1 Introduction
6.2 Existence of Solutions
6.3 Bisection Method
6.4 False Position Method
6.5 Newton–Raphson Method
6.6 Secant Method
6.7 Fixed‐Point Iteration Method
6.8 Visual Solution: Code6
6.9 Summary
6.10 Numerical Exercises
6.11 Programming Challenges
7-Interpolation and Approximation
7.1 Curve Fitting
7.2 Lagrange Interpolation
7.3 Newton Interpolations
7.4 Cubic Spline
7.5 Least‐Squares Approximation
7.6 Visual Solution: Code7
7.7 Summary
7.8 Numerical Exercises
7.9 Programming Challenges
8-Differentiation and Integration
8.1 Introduction
8.2 Numerical Differentiation
8.3 Numerical Integration
8.4 Visual Solution: Code8
8.5 Summary
8.6 Numerical Exercises
8.7 Programming Challenges
9-Eigenvalues and Eigenvectors
9.1 Eigenvalues and Their Significance
9.2 Exact Solution and Its Existence
9.3 Power Method
9.4 Shifted Power Method
9.5 QR Method
9.6 Visual Solution: Code9
9.7 Summary
9.8 Numerical Exercises
9.9 Programming Challenges
10-Ordinary Differential Equations
10.1 Introduction
10.2 Initial‐Value Problem for First‐Order ODE
10.3 Taylor Series Method
10.4 Runge–Kutta of Order 2 Method
10.5 Runge–Kutta of Order 4 Method
10.6 Predictor‐Corrector Multistep Method
10.7 System of First‐Order ODEs
10.8 Second‐Order ODE
10.9 Initial‐Value Problem for Second‐Order ODE
10.10 Finite‐Difference Method for Second‐Order ODE
10.11 Differentiated Boundary Conditions
10.12 Visual Solution: Code10
10.13 Summary
10.14 Numerical Exercises
10.15 Programming Challenges
11-Partial Differential Equations
11.1 Introduction
11.2 Poisson's Equation
11.3 Laplace's Equation
11.4 Heat Equation
11.5 Wave Equation
11.6 Visual Solution: Code11
11.7 Summary
11.8 Numerical Exercises
11.9 Programming Exercises
-Index |
Computing for Numerical Methods Using Visual C++ [texte imprimé] / Salleh Shaharuddin, Auteur ; Albert Y. Zomaya, Auteur ; Sakhinah Abu Bakar, Auteur . - USA : John wiley & Sons, 2008 . - 448 p. : couv. ill. en coul. ; 25 cm. ISBN : 978-0-470-12795-7 Langues : Anglais ( eng) | Catégories : | INFORMATIQUE
| | Index. décimale : | 08-02 Logiciels et programmation | | Résumé : | 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++
| | Note de contenu : | Contents
1-Modeling and Simulation
1.1 Numerical Approximation
1.2 C++ for Numerical Modeling
1.3 Mathematical Modeling
1.4 Simulation and Its Visualization
1.5 Numerical Methods
1.6 Numerical Applications
2-Fundamental Tools for Mathematical Computing
2.1 C++ for High‐Performance Computing
2.2 Dynamic Memory Allocation
2.3 Matrix Reduction Problems
2.4 Matrix Algebra
2.5 Algebra of Complex Numbers
2.6 Number Sorting
Summary
Programming Challenges
3-Numerical Interface Designs
3.1 Microsoft Foundation Classes
3.2 Graphics Device Interface
3.4 Writing a Basic Windows Program
3.5 Displaying Text and Graphics
3.6 Events and Methods
3.7 Standard Control Resources
3.8 Menu and File I/O
3.9 Keyboard Control
3.10 MFC Compatibility with .Net
Summary
4-Curve Visualization
4.1 Tools for Visualization
4.2 MyParser
4.3 Drawing Curves
4.4 Generating Curves Using MyParser
4.5 Summary
4.6 Programming Challenges
5-Systems of Linear Equations
5.1 Introduction
5.2 Existence of Solutions
5.3 Gaussian Elimination Techniques
5.4 LU Factorization Methods
5.5 Iterative Techniques
5.6 Visualizing the Solution: Code5
5.7 Summary
5.8 Numerical Exercises
5.9 Programming Challenges
6-Nonlinear Equations
6.1 Introduction
6.2 Existence of Solutions
6.3 Bisection Method
6.4 False Position Method
6.5 Newton–Raphson Method
6.6 Secant Method
6.7 Fixed‐Point Iteration Method
6.8 Visual Solution: Code6
6.9 Summary
6.10 Numerical Exercises
6.11 Programming Challenges
7-Interpolation and Approximation
7.1 Curve Fitting
7.2 Lagrange Interpolation
7.3 Newton Interpolations
7.4 Cubic Spline
7.5 Least‐Squares Approximation
7.6 Visual Solution: Code7
7.7 Summary
7.8 Numerical Exercises
7.9 Programming Challenges
8-Differentiation and Integration
8.1 Introduction
8.2 Numerical Differentiation
8.3 Numerical Integration
8.4 Visual Solution: Code8
8.5 Summary
8.6 Numerical Exercises
8.7 Programming Challenges
9-Eigenvalues and Eigenvectors
9.1 Eigenvalues and Their Significance
9.2 Exact Solution and Its Existence
9.3 Power Method
9.4 Shifted Power Method
9.5 QR Method
9.6 Visual Solution: Code9
9.7 Summary
9.8 Numerical Exercises
9.9 Programming Challenges
10-Ordinary Differential Equations
10.1 Introduction
10.2 Initial‐Value Problem for First‐Order ODE
10.3 Taylor Series Method
10.4 Runge–Kutta of Order 2 Method
10.5 Runge–Kutta of Order 4 Method
10.6 Predictor‐Corrector Multistep Method
10.7 System of First‐Order ODEs
10.8 Second‐Order ODE
10.9 Initial‐Value Problem for Second‐Order ODE
10.10 Finite‐Difference Method for Second‐Order ODE
10.11 Differentiated Boundary Conditions
10.12 Visual Solution: Code10
10.13 Summary
10.14 Numerical Exercises
10.15 Programming Challenges
11-Partial Differential Equations
11.1 Introduction
11.2 Poisson's Equation
11.3 Laplace's Equation
11.4 Heat Equation
11.5 Wave Equation
11.6 Visual Solution: Code11
11.7 Summary
11.8 Numerical Exercises
11.9 Programming Exercises
-Index |
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