## Applied Numerical Methods Using Matlab

Rs699

Publisher

### Wiley India Pvt Ltd

Publication Year 2007
ISBN-13

### ISBN 9788126514151

ISBN-10 8126514159
Binding

#### Paperback

Number of Pages 528 Pages
Language (English)
Subject

#### Electronics & Communication Engineering

The objective of this book is to make use of the powerful MATLAB software to avoid complex derivations and to teach the fundamental concepts using the software to solve practical problems. The authors use a more practical approach and link every method to real engineering and/or science problems. The main idea is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems.

Won Y. Yang PhD, is Professor of Electrical Engineering at Chung-Ang University, Korea. Wenwu Cao, PhD, is Professor of Mathematics and Materials Science at The Pennsylvania State University.

Tae-Sang Chung PhD, is Professor of Electrical Engineering at Chung-Ang University, Korea.

John Morris PhD, is Associate Professor of Computer Science and Electrical and Computer Engineering at The University of Auckland, New Zealand.

Preface 1. MATLAB Usage and Computational Errors

Basic Operations of MATLAB
Input/Output of Data from MATLAB Command Window
Input/Output of Data Through Files
Input/Output of Data Using Keyboard
2-D Graphic Input/Output
3-D Graphic Output
Mathematical Functions
Operations on Vectors and Matrices
Random Number Generators
Flow Control
Computer Errors Versus Human Mistakes
IEEE 64-bit Floating-Point Number Representation
Various Kinds of Computing Errors
Absolute/Relative Computing Errors
Error Propagation
Tips for Avoiding Large Errors
Toward Good Program
Nested Computing for Computational Efficiency
Vector Operation Versus Loop Iteration
Iterative Routine Versus Nested Routine
To Avoid Runtime Error
Parameter Sharing via Global Variables
Parameter Passing Through Varargin
2. System of Linear Equations

Solution for a System of Linear Equations
The Nonsingular Case (M = N)
The Underdetermined Case (M < N): Minimum-Norm Solution
The Overdetermined Case (M > N): Least-Squares Error Solution
RLSE (Recursive Least-Squares Estimation)
Solving a System of Linear Equations
Gauss Elimination
Partial Pivoting
Gauss-Jordan Elimination
Inverse Matrix
Decomposition (Factorization)
LU Decomposition (Factorization): Triangularization
Other Decomposition (Factorization): Cholesky, QR and SVD
Iterative Methods to Solve Equations
Jacobi Iteration
Gauss-Seidel Iteration
The Convergence of Jacobi and Gauss-Seidel Iterations
3. Interpolation and Curve Fitting

Interpolation by Lagrange Polynomial
Interpolation by Newton Polynomial
Approximation by Chebyshev Polynomial
Interpolation by Cubic Spline
Hermite Interpolating Polynomial
Two-dimensional Interpolation
Curve Fitting
Straight Line Fit: A Polynomial Function of First Degree
Polynomial Curve Fit: A Polynomial Function of Higher Degree
Exponential Curve Fit and Other Functions
Fourier Transform
FFT Versus DFT
Physical Meaning of DFT
Interpolation by Using DFS
4. Nonlinear Equations

Iterative Method Toward Fixed Point
Bisection Method
False Position or Regula Falsi Method
Newton(-Raphson) Method
Secant Method
Newton Method for a System of Nonlinear Equations
Symbolic Solution for Equations
A Real-World Problem
5. Numerical Differentiation/Integration

Difference Approximation for First Derivative
Approximation Error of First Derivative
Difference Approximation for Second and Higher Derivative
Interpolating Polynomial and Numerical Differential
Trapezoidal Method and Simpson Method
Recursive Rule and Romberg Integration
Gauss-Legendre Integration
Gauss-Hermite Integration
Gauss-Laguerre Integration
Gauss-Chebyshev Integration
Double Integral
6. Ordinary Differential Equations

Eulers Method
Heuns Method: Trapezoidal Method
Runge-Kutta Method
Predictor-Corrector Method
Hamming Method
Comparison of Methods
Vector Differential Equations
State Equation
Discretization of LTI State Equation
High-Order Differential Equation to State Equation
Stiff Equation
Boundary Value Problem (BVP)
Shooting Method
Finite Difference Method
7. Optimization

Unconstrained Optimization [L-2, Chapter 7]
Golden Search Method
Steepest Descent Method
Newton Method
Simulated Annealing Method [W-7]
Genetic Algorithm [W-7]
Constrained Optimization [L-2, Chapter 10]
Lagrange Multiplier Method
Penalty Function Method
MATLAB Built-In Routines for Optimization
Unconstrained Optimization
Constrained Optimization
Linear Programming (LP)
8. Matrices and Eigenvalues

Eigenvalues and Eigenvectors
Similarity Transformation and Diagonalization
Power Method
Scaled Power Method
Inverse Power Method
Shifted Inverse Power Method
Jacobi Method
Physical Meaning of Eigenvalues/Eigenvectors
Eigenvalue Equations
9. Partial Differential Equations

Elliptic PDE
Parabolic PDE
The Explicit Forward Euler Method
The Implicit Backward Euler Method
The Crank-Nicholson Method
Two-Dimensional Parabolic PDE
Hyperbolic PDE
The Explicit Central Difference Method
Two-Dimensional Hyperbolic PDE
Finite Element Method (FEM) for solving PDE
GUI of MATLAB for Solving PDEs: PDETOOL
Basic PDEs Solvable by PDETOOL
The Usage of PDETOOL
Examples of Using PDETOOL to Solve PDEs

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