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Numerical Methods Using MATLAB

ISBN-10: 0123869420
ISBN-13: 9780123869425
Edition: 3rd 2012
List price: $57.99 Buy it from $21.75
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Description: 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.  More...

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Book details

List price: $57.99
Edition: 3rd
Copyright year: 2012
Publisher: Elsevier Science & Technology
Publication date: 8/21/2012
Binding: Paperback
Pages: 552
Size: 7.75" wide x 9.25" long x 1.25" tall
Weight: 2.486
Language: English

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 exercises and solutions to illustrate how numerical methods can be used to study problems which have applications in the biosciences, chaos, optimization, engineering and science across the board.Over 500 numerical algorithms, their fundamental principles, and applicationsGraphs are used extensively to clarify the complexity of problemsIncludes coded genetic algorithmsIncludes the lagrange multiplier methodUser-friendly and written in a conversational style

Preface
List of Figures
An Introduction to Matlab�
The Matlab Software Package
Matrices and Matrix Operations in Matlab
Manipulating the Elements of a Matrix
Transposing Matrices
Special Matrices
Generating Matrices and Vectors with Specified Element Values
Matrix Functions
Using the Matlab \ Operator for Matrix Division
Element-by-Element Operations
Scalar Operations and Functions
String Variables
Input and Output in Matlab
Matlab Graphics
Three-Dimensional Graphics
Manipulating Graphics-Handle Graphics
Scripting in Matlab
User-Defined Functions in Matlab
Data Structures in Matlab
Editing Matlab Scripts
Some Pitfalls in Matlab
Faster Calculations in Matlab
Problems
Linear Equations and Eigensystems
Introduction
linear Equation Systems
Operators \ and / for Solving Ax = b
Accuracy of Solutions and Ill-Conditioning
Elementary Row Operations
Solution of Ax = b by Gaussian Elimination
LU Decomposition
Cholesky Decomposition
QR Decomposition
Singular Value Decomposition
The Pseudo-Inverse
Over- and Underdetermined Systems
Iterative Methods
Sparse Matrices
The Eigenvalue Problem
Iterative Methods for Solving the Eigenvalue Problem
The Matlab Function eig
Summary
Problems
Solution of Nonlinear Equations
Introduction
The Nature of Solutions to Nonlinear Equations
The Bisection Algorithm
Iterative or Fixed Point Methods
The Convergence of Iterative Methods
Ranges for Convergence and Chaotic Behavior
Newton's Method
Schroder's Method
Numerical Problems
The Matlab Function fzero and Comparative Studies
Methods for Finding All the Roots of a Polynomial
Solving Systems of Nonlinear Equations
Broyden's Method for Solving Nonlinear Equations
Comparing the Newton and Broyden Methods
Summary
Problems
Differentiation and Integration
Introduction
Numerical Differentiation
Numerical Integration
Simpson's Rule
Newton-Cotes Formulae
Romberg Integration
Gaussian Integration
Infinite Ranges of Integration
Gauss-Chebyshev Formula
Gauss-Lobatto Integration
Filon's Sine and Cosine Formulae
Problems in the Evaluation of Integrals
Test Integrals
Repeated Integrals
Matlab Functions for Double and Triple Integration
Summary
Problems
Solution of Differential Equations
Introduction
Euler's Method
The Problem of Stability
The Trapezoidal Method
Runge-Kutta Methods
Predictor-Corrector Methods
Hamming's Method and the Use of Error Estimates
Error Propagation in Differential Equations
The Stability of Particular Numerical Methods
Systems of Simultaneous Differential Equations
The Lorenz Equations
The Predator-Prey Problem
Differential Equations Applied to Neural Networks
Higher-Order Differential Equations
Stiff Equations
Special Techniques
Extrapolation Techniques
Summary
Problems
Boundary Value Problems
Classification of Second-Order Partial Differential Equations
The Shooting Method
The Finite Difference Method
Two-Point Boundary Value Problems
Parabolic Partial Differential Equations
Hyperbolic Partial Differential Equations
Elliptic Partial Differential Equations
Summary
Problems
Fitting Functions to Data
Introduction
Interpolation Using Polynomials
Interpolation Using Splines
Fourier Analysis of Discrete Data
Multiple Regression: Least Squares Criterion
Diagnostics for Model Improvement
Analysis of Residuals
Polynomial Regression
Fitting General Functions to Data
Nonlinear Least Squares Regression
Transforming Data
Summary
Problems
Optimization Methods
Introduction
Linear Programming Problems
Optimizing Single-Variable Functions
The Conjugate Gradient Method
Moller's Scaled Conjugate Gradient Method
Conjugate Gradient Method for Solving Linear Systems
Genetic Algorithms
Continuous Genetic Algorithm
Simulated Annealing
Constrained Nonlinear Optimization
The Sequential Unconstrained Minimization Technique
Summary
Problems
Applications of the Symbolic Toolbox
Introduction to the Symbolic Toolbox
Symbolic Variables and Expressions
Variable-Precision Arithmetic in Symbolic Calculations
Series Expansion and Summation
Manipulation of Symbolic Matrices
Symbolic Methods for the Solution of Equations
Special Functions
Symbolic Differentiation
Symbolic Partial Differentiation
Symbolic Integration
Symbolic Solution of Ordinary Differential Equations
The Laplace Transform
The Z-Transform
Fourier Transform Methods
Linking Symbolic and Numerical Processes
Summary
Problems
Appendices
Matrix Algebra
Introduction
Matrices and Vectors
Some Special Matrices
Determinants
Matrix Operations
Complex Matrices
Matrix Properties
Some Matrix Relationships
Eigenvalues
Definition of Norms
Reduced Row Echelon Form
Differentiating Matrices
Square Root of a Matrix
Error Analysis
Introduction
Errors in Arithmetic Operations
Errors in the Solution of Linear Equation Systems
Solutions to Selected Problems
Bibliography
Index

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