Applied Numerical Methods Using MATLAB. Won Y. Yang

      1  Cover

      2  Preface

      3  Acknowledgments

      4  About the Companion Website

      5  1 MATLAB Usage and Computational Errors 1.1 Basic Operations of MATLAB 1.2 Computer Errors vs. Human Mistakes 1.3 Toward Good Program Problems

      6  2 System of Linear Equations 2.1 Solution for a System of Linear Equations 2.2 Solving a System of Linear Equations 2.3 Inverse Matrix 2.4 Decomposition (Factorization) 2.5 Iterative Methods to Solve Equations Problems

      7  3 Interpolation and Curve Fitting 3.1 Interpolation by Lagrange Polynomial 3.2 Interpolation by Newton Polynomial 3.3 Approximation by Chebyshev Polynomial 3.4 Pade Approximation by Rational Function 3.5 Interpolation by Cubic Spline 3.6 Hermite Interpolating Polynomial 3.7 Two‐Dimensional Interpolation 3.8 Curve Fitting 3.9 Fourier Transform

      8  4 Nonlinear Equations 4.1 Iterative Method toward Fixed Point 4.2 Bisection Method 4.3 False Position or Regula Falsi Method 4.4 Newton(‐Raphson) Method 4.5 Secant Method 4.6 Newton Method for a System of Nonlinear Equations 4.7 Bairstow's Method for a Polynomial Equation 4.8 Symbolic Solution for Equations 4.9 Real‐World Problems

      9  5 Numerical Differentiation/Integration 5.1 Difference Approximation for the First Derivative 5.2 Approximation Error of the First Derivative 5.3 Difference Approximation for Second and Higher Derivative 5.4 Interpolating Polynomial and Numerical Differential 5.5 Numerical Integration and Quadrature 5.6 Trapezoidal Method and Simpson Method 5.7 Recursive Rule and Romberg Integration 5.8 Adaptive Quadrature 5.9 Gauss Quadrature 5.10 Double Integral 5.11 Integration Involving PWL Function

      10  6 Ordinary Differential Equations 6.1 Euler's Method 6.2 Heun's Method – Trapezoidal Method 6.3 Runge‐Kutta Method 6.4 Predictor‐Corrector Method 6.5 Vector Differential Equations 6.6 Boundary Value Problem (BVP) Problems

      11  7 Optimization 7.1 Unconstrained Optimization 7.2 Constrained Optimization 7.3 MATLAB Built‐In Functions for Optimization 7.4 Neural Network[K‐1] 7.5 Adaptive Filter^[Y‐3] 7.6 Recursive Least Square Estimation (RLSE)^[Y‐3]

      12  8 Matrices and Eigenvalues 8.1 Eigenvalues and Eigenvectors 8.2 Similarity Transformation and Diagonalization 8.3 Power Method 8.4 Jacobi Method 8.5 Gram‐Schmidt Orthonormalization and QR Decomposition 8.6