Numerical Methods: Using MATLAB, Fourth Edition (Complete Instructor's Resources with Solution Manual) (Solutions)

Cover
Numerical Methods: Using MATLAB
Copyright
Dedication
List of Figures
About the Authors
Preface
Acknowledgment
1 An Introduction to Matlab®
	1.1 The Software Package Matlab
	1.2 Matrices 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 Algebra in Matlab
	1.8 Matrix Functions
	1.9 Using the Matlab Operator for Matrix Division
	1.10 Element-by-Element Operations
	1.11 Scalar Operations and Functions
	1.12 String Variables
	1.13 Input and Output in Matlab
	1.14 Matlab Graphics
	1.15 Three-Dimensional Graphics
	1.16 Implicit Graphics
	1.17 Manipulating Graphics - Handle Graphics
	1.18 Scripting in Matlab
	1.19 User-Defined Functions in Matlab
	1.20 Data Structures in Matlab
	1.21 Editing Matlab Scripts
	1.22 Some Pitfalls in Matlab
	1.23 Speeding up Calculations in Matlab
	1.24 Live Editor
	1.25 Summary
	1.26 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 Under-Determined Systems
	2.13 Iterative Methods
	2.14 Sparse Matrices
	2.15 The Eigenvalue Problem
		2.15.1 Eigenvalue Decomposition
		2.15.2 Comparing Eigenvalue and Singular Value Decomposition
	2.16 Iterative Methods for Solving the Eigenvalue Problem
	2.17 Solution of the General Eigenvalue Problem
	2.18 The Google `PageRank' Algorithm
	2.19 Summary
	2.20 Problems
3 Solution of Non-Linear Equations
	3.1 Introduction
	3.2 The Nature of Solutions to Non-Linear 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 Non-Linear Equations
	3.13 Broyden's Method for Solving Non-Linear Equations
	3.14 Comparing the Newton and Broyden Methods
	3.15 Summary
	3.16 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 Adaptive Integration
	4.13 Problems in the Evaluation of Integrals
	4.14 Test Integrals
	4.15 Repeated Integrals
		4.15.1 Simpson's Rule for Repeated Integrals
		4.15.2 Gaussian Integration for Repeated Integrals
	4.16 Matlab Functions for Double and Triple Integration
	4.17 Summary
	4.18 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
		5.10.1 Zeeman Model
		5.10.2 The Predator-Prey Problem
	5.11 Higher-Order Differential Equations
		5.11.1 Conversion to a Set of Simultaneous First-Order Differential Equations
		5.11.2 Newmark's Method
	5.12 Chaotic Systems
		5.12.1 The Lorenz Equations
		5.12.2 Duffing's Equation
	5.13 Differential Equations Applied to Neural Networks
	5.14 Stiff Equations
	5.15 Special Techniques
	5.16 Extrapolation Techniques
	5.17 Simulink
	5.18 Summary
	5.19 Problems
6 Boundary Value Problems
	6.1 Classification of Second-Order 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
	6.9 Problems
7 Analyzing Data
	7.1 Introduction
	7.2 Interpolation Using Polynomials
	7.3 Interpolation Using Splines
	7.4 Multiple Regression: Least Squares Criterion
	7.5 Diagnostics for Model Improvement
	7.6 Analysis of Residuals
	7.7 Polynomial Regression
	7.8 Fitting General Functions to Data
	7.9 Non-Linear Least Squares Regression
	7.10 Transforming Data
	7.11 The Kalman Filter
	7.12 Principal Component Analysis
	7.13 Summary
	7.14 Problems
8 Analyzing Data Using Discrete Transforms
	8.1 Introduction
	8.2 Fourier Analysis of Discrete Data
	8.3 The Hilbert Transform
	8.4 The Walsh Transforms
	8.5 Introduction to Wavelet Analysis
	8.6 Discrete Wavelet Transforms
		8.6.1 Haar Wavelet
		8.6.2 Daubechies Wavelets
	8.7 Continuous Wavelet Transforms
	8.8 Summary
	8.9 Problems
9 Optimization Methods
	9.1 Introduction
	9.2 Linear Programming Problems
	9.3 Optimizing Single-Variable Functions
	9.4 The Conjugate Gradient Method
	9.5 Moller's Scaled Conjugate Gradient Method
	9.6 Conjugate Gradient Method for Solving Linear Systems
	9.7 Metaheuristic Methods
	9.8 Simulated Annealing
	9.9 Evolutionary Algorithm
	9.10 Differential Evolution
	9.11 Constrained Non-Linear Optimization
	9.12 The Sequential Unconstrained Minimization Technique
	9.13 Summary
	9.14 Problems
10 Applications of the Symbolic Toolbox
	10.1 Introduction to the Symbolic Toolbox
	10.2 Symbolic Variables and Expressions
	10.3 Variable Precision Arithmetic in Symbolic Calculations
	10.4 Series Expansion and Summation
	10.5 Manipulation of Symbolic Matrices
	10.6 Symbolic Methods for the Solution of Equations
	10.7 Special Functions
	10.8 Symbolic Differentiation
	10.9 Symbolic Partial Differentiation
	10.10 Symbolic Integration
	10.11 Symbolic Solution of Ordinary Differential Equations
	10.12 The Laplace Transform
	10.13 The Z-Transform
	10.14 Fourier Transform Methods
	10.15 Linking Symbolic and Numerical Processes
	10.16 Summary
	10.17 Problems
APPENDIX
A Matrix Algebra
	A.1 Introduction
	A.2 Matrices and Vectors
	A.3 Some Special Matrices
	A.4 Determinants
	A.5 Matrix Operations
	A.6 Complex Matrices
	A.7 Matrix Properties
	A.8 Some Matrix Relationships
	A.9 Eigenvalues
	A.10 Definition of Norms
	A.11 Reduced Row Echelon Form
	A.12 Differentiating Matrices
	A.13 Square Root of a Matrix
APPENDIX
B Error Analysis
	B.1 Introduction
	B.2 Errors in Arithmetic Operations
	B.3 Errors in the Solution of Linear Equation Systems
Solutions to Selected Problems
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 10
Bibliography
Index
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