Читать книгу Applied Numerical Methods Using MATLAB - Won Y. Yang - Страница 2
Table of Contents
Оглавление1 Cover
2 Preface
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 Physical Meaning of Eigenvalues/Eigenvectors 8.7 Differential Equations with Eigenvectors 8.8 DoA Estimation with Eigenvectors[Y-3]
13 9 Partial Differential Equations 9.1 Elliptic PDE 9.2 Parabolic PDE 9.3 Hyperbolic PDES 9.4 Finite Element Method (FEM) for Solving PDE 9.5 GUI of MATLAB for Solving PDES – PDEtool
14 Appendix A: Appendix AMean Value TheoremMean Value Theorem
15 Appendix B: Appendix BMatrix Operations/PropertiesMatrix Operations/Properties B.1 Addition and Subtraction B.2 Multiplication B.3 Determinant B.4 Eigenvalues and Eigenvectors of a Matrix1 B.5 Inverse Matrix B.6 Symmetric/Hermitian Matrix B.7 Orthogonal/Unitary Matrix B.8 Permutation Matrix B.9 Rank B.10 Row Space and Null Space B.11 Row Echelon Form B.12 Positive Definiteness B.13 Scalar (Dot) Product and Vector (Cross) Product B.14 Matrix Inversion Lemma
16 Appendix C: Appendix CDifferentiation W.R.T. A VectorDifferentiation W.R.T. A Vector
17 Appendix D: Appendix DLaplace TransformLaplace Transform
18 Appendix E: Appendix EFourier TransformFourier Transform
19 Appendix F: Appendix FUseful FormulasUseful Formulas
20 Appendix G: Appendix GSymbolic ComputationSymbolic Computation G.1 How to Declare Symbolic Variables and Handle Symbolic Expressions G.2 Calculus G.3 Linear Algebra G.4 Solving Algebraic Equations G.5 Solving Differential Equations
21 Appendix H: Appendix HSparse MatricesSparse Matrices
22 Appendix I: Appendix IMATLABMATLAB
23 References
24 Index
