Applied Numerical Methods Using Matlab

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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 realengineering 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.

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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. Table of Contents 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 Adaptive Input Argument List 2. System of Linear Equations Solution for a System of Linear Equations The Nonsingular Case (M = N) The Underdetermined Case (M 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 Pade Approximation by Rational Function 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 Numerical Integration and Quadrature Trapezoidal Method and Simpson Method Recursive Rule and Romberg Integration Adaptive Quadrature Gauss Quadrature 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 Adams-Bashforth-Moulton 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 Quadratic Approximation Method Nelder-Mead Method [W-8] Steepest Descent Method Newton Method Conjugate Gradient 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