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Numerical Methods : Using MATLAB.
Numerical Methods using MATLAB, 3rd edition is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exerc...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Elsevier Science,
2012.
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| Edición: | 3rd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover
- Numerical Methods Using Matlab®
- Copyright
- Dedication
- Table of Contents
- Preface
- List of Figures
- 1 An Introduction to Matlab®
- 1.1 The Matlab Software Package
- 1.2 Matrices and Matrix Operations in Matlab
- 1.3 Manipulating the Elements of a Matrix
- 1.4 Transposing Matrices
- 1.5 Special Matrices
- 1.6 Generating Matrices and Vectors with Specified Element Values
- 1.7 Matrix Functions
- 1.8 Using the Matlab \ Operator for Matrix Division
- 1.9 Element-by-Element Operations
- 1.10 Scalar Operations and Functions
- 1.11 String Variables
- 1.12 Input and Output in Matlab
- 1.13 Matlab Graphics
- 1.14 Three-Dimensional Graphics
- 1.15 Manipulating Graphics-Handle Graphics
- 1.16 Scripting in Matlab
- 1.17 User-Defined Functions in Matlab
- 1.18 Data Structures in Matlab
- 1.19 Editing Matlab Scripts
- 1.20 Some Pitfalls in Matlab
- 1.21 Faster Calculations in Matlab
- Problems
- 2 Linear Equations and Eigensystems
- 2.1 Introduction
- 2.2 Linear Equation Systems
- 2.3 Operators \ and / for Solving Ax = b
- 2.4 Accuracy of Solutions and Ill-Conditioning
- 2.5 Elementary Row Operations
- 2.6 Solution of Ax = b by Gaussian Elimination
- 2.7 LU Decomposition
- 2.8 Cholesky Decomposition
- 2.9 QR Decomposition
- 2.10 Singular Value Decomposition
- 2.11 The Pseudo-Inverse
- 2.12 Over- and Underdetermined Systems
- 2.13 Iterative Methods
- 2.14 Sparse Matrices
- 2.15 The Eigenvalue Problem
- 2.16 Iterative Methods for Solving the Eigenvalue Problem
- 2.17 The Matlab Function eig
- 2.18 Summary
- Problems
- 3 Solution of Nonlinear Equations
- 3.1 Introduction
- 3.2 The Nature of Solutions to Nonlinear Equations
- 3.3 The Bisection Algorithm
- 3.4 Iterative or Fixed Point Methods
- 3.5 The Convergence of Iterative Methods
- 3.6 Ranges for Convergence and Chaotic Behavior.
- 3.7 Newton's Method
- 3.8 Schroder's Method
- 3.9 Numerical Problems
- 3.10 The Matlab Function fzero and Comparative Studies
- 3.11 Methods for Finding All the Roots of a Polynomial
- 3.11.1 Bairstow's Method
- 3.11.2 Laguerre's Method
- 3.12 Solving Systems of Nonlinear Equations
- 3.13 Broyden's Method for Solving Nonlinear Equations
- 3.14 Comparing the Newton and Broyden Methods
- 3.15 Summary
- Problems
- 4 Differentiation and Integration
- 4.1 Introduction
- 4.2 Numerical Differentiation
- 4.3 Numerical Integration
- 4.4 Simpson's Rule
- 4.5 Newton-Cotes Formulae
- 4.6 Romberg Integration
- 4.7 Gaussian Integration
- 4.8 Infinite Ranges of Integration
- 4.8.1 Gauss-Laguerre Formula
- 4.8.2 Gauss-Hermite Formula
- 4.9 Gauss-Chebyshev Formula
- 4.10 Gauss-Lobatto Integration
- 4.11 Filon's Sine and Cosine Formulae
- 4.12 Problems in the Evaluation of Integrals
- 4.13 Test Integrals
- 4.14 Repeated Integrals
- 4.14.1 Simpson's Rule for Repeated Integrals
- 4.14.2 Gaussian Integration for Repeated Integrals
- 4.15 Matlab Functions for Double and Triple Integration
- 4.16 Summary
- Problems
- 5 Solution of Differential Equations
- 5.1 Introduction
- 5.2 Euler's Method
- 5.3 The Problem of Stability
- 5.4 The Trapezoidal Method
- 5.5 Runge-Kutta Methods
- 5.6 Predictor-Corrector Methods
- 5.7 Hamming's Method and the Use of Error Estimates
- 5.8 Error Propagation in Differential Equations
- 5.9 The Stability of Particular Numerical Methods
- 5.10 Systems of Simultaneous Differential Equations
- 5.11 The Lorenz Equations
- 5.12 The Predator-Prey Problem
- 5.13 Differential Equations Applied to Neural Networks
- 5.14 Higher-Order Differential Equations
- 5.15 Stiff Equations
- 5.16 Special Techniques
- 5.17 Extrapolation Techniques
- 5.18 Summary
- Problems
- 6 Boundary Value Problems.
- 6.1 Classification of Second-Order Partial Differential Equations
- 6.2 The Shooting Method
- 6.3 The Finite Difference Method
- 6.4 Two-Point Boundary Value Problems
- 6.5 Parabolic Partial Differential Equations
- 6.6 Hyperbolic Partial Differential Equations
- 6.7 Elliptic Partial Differential Equations
- 6.8 Summary
- Problems
- 7 Fitting Functions to Data
- 7.1 Introduction
- 7.2 Interpolation Using Polynomials
- 7.3 Interpolation Using Splines
- 7.4 Fourier Analysis of Discrete Data
- 7.5 Multiple Regression: Least Squares Criterion
- 7.6 Diagnostics for Model Improvement
- 7.7 Analysis of Residuals
- 7.8 Polynomial Regression
- 7.9 Fitting General Functions to Data
- 7.10 Nonlinear Least Squares Regression
- 7.11 Transforming Data
- 7.12 Summary
- Problems
- 8 Optimization Methods
- 8.1 Introduction
- 8.2 Linear Programming Problems
- 8.3 Optimizing Single-Variable Functions
- 8.4 The Conjugate Gradient Method
- 8.5 Moller's Scaled Conjugate Gradient Method
- 8.6 Conjugate Gradient Method for Solving Linear Systems
- 8.7 Genetic Algorithms
- 8.8 Continuous Genetic Algorithm
- 8.9 Simulated Annealing
- 8.10 Constrained Nonlinear Optimization
- 8.11 The Sequential Unconstrained Minimization Technique
- 8.12 Summary
- Problems
- 9 Applications of the Symbolic Toolbox
- 9.1 Introduction to the Symbolic Toolbox
- 9.2 Symbolic Variables and Expressions
- 9.3 Variable-Precision Arithmetic in Symbolic Calculations
- 9.4 Series Expansion and Summation
- 9.5 Manipulation of Symbolic Matrices
- 9.6 Symbolic Methods for the Solution of Equations
- 9.7 Special Functions
- 9.8 Symbolic Differentiation
- 9.9 Symbolic Partial Differentiation
- 9.10 Symbolic Integration
- 9.11 Symbolic Solution of Ordinary Differential Equations
- 9.12 The Laplace Transform
- 9.13 The Z-Transform.