Applied Numerical Methods Using MATLAB

Applied Numerical Methods Using MATLAB

"This book makes use of MATLAB software to teach the fundamental concepts using the software to solve practical engineering and/or science problems. The programs are presented in a complete form so that readers can run them instantly with no programming skill, allowing them to focus on understa...

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Bibliographic Details
Main Author: Yang, Won Y. (-)
Other Authors: Cao, Wenwu, Kim, Jaekwon, Park, Kyung W., Park, Ho-Hyun, Joung, Jingon, Ro, Jong-Suk, Lee, Han L., Hong, Cheol-Ho, Im, Taeho
Format: eBook
Language:Inglés
Published: Newark : John Wiley & Sons, Incorporated 2020.
Edition:2nd ed
Subjects:
MATLAB.
Numerical analysis > Data processing.
See on Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009849086406719
Table of Contents:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • About the Companion Website
  • Chapter 1 MATLAB Usage and Computational Errors
  • 1.1 Basic Operations of MATLAB
  • 1.1.1 Input/Output of Data from MATLAB Command Window
  • 1.1.2 Input/Output of Data Through Files
  • 1.1.3 Input/Output of Data Using Keyboard
  • 1.1.4 Two‐Dimensional (2D) Graphic Input/Output
  • 1.1.5 Three Dimensional (3D) Graphic Output
  • 1.1.6 Mathematical Functions
  • 1.1.7 Operations on Vectors and Matrices
  • 1.1.8 Random Number Generators
  • 1.1.9 Flow Control
  • 1.2 Computer Errors vs. Human Mistakes
  • 1.2.1 IEEE 64‐bit Floating‐Point Number Representation
  • 1.2.2 Various Kinds of Computing Errors
  • 1.2.3 Absolute/Relative Computing Errors
  • 1.2.4 Error Propagation
  • 1.2.5 Tips for Avoiding Large Errors
  • 1.3 Toward Good Program
  • 1.3.1 Nested Computing for Computational Efficiency
  • 1.3.2 Vector Operation vs. Loop Iteration
  • 1.3.3 Iterative Routine vs. Recursive Routine
  • 1.3.4 To Avoid Runtime Error
  • 1.3.5 Parameter Sharing via GLOBAL Variables
  • 1.3.6 Parameter Passing Through VARARGIN
  • 1.3.7 Adaptive Input Argument List
  • Chapter 2 System of Linear Equations
  • 2.1 Solution for a System of Linear Equations
  • 2.1.1 The Nonsingular Case (M &amp
  • equals
  • N)
  • 2.1.2 The Underdetermined Case (M &lt
  • N): Minimum‐norm Solution
  • 2.1.3 The Overdetermined Case (M &gt
  • N): Least‐squares Error Solution
  • 2.1.4 Recursive Least‐Squares Estimation (RLSE)
  • 2.2 Solving a System of Linear Equations
  • 2.2.1 Gauss(ian) Elimination
  • 2.2.2 Partial Pivoting
  • 2.2.3 Gauss‐Jordan Elimination
  • 2.3 Inverse Matrix
  • 2.4 Decomposition (Factorization)
  • 2.4.1 LU Decomposition (Factorization) - Triangularization
  • 2.4.2 Other Decomposition (Factorization) - Cholesky, QR and SVD
  • 2.5 Iterative Methods to Solve Equations.
  • 2.5.1 Jacobi Iteration
  • 2.5.2 Gauss‐Seidel Iteration
  • 2.5.3 The Convergence of Jacobi and Gauss‐Seidel Iterations
  • Chapter 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
  • 3.8.1 Straight‐Line Fit - A Polynomial Function of Degree 1
  • 3.8.2 Polynomial Curve Fit - A Polynomial Function of Higher Degree
  • 3.8.3 Exponential Curve Fit and Other Functions
  • 3.9 Fourier Transform
  • 3.9.1 FFT vs. DFT
  • 3.9.2 Physical Meaning of DFT
  • 3.9.3 Interpolation by Using DFS
  • Chapter 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
  • Chapter 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
  • 5.9.1 Gauss‐Legendre Integration
  • 5.9.2 Gauss‐Hermite Integration
  • 5.9.3 Gauss‐Laguerre Integration
  • 5.9.4 Gauss‐Chebyshev Integration
  • 5.10 Double Integral
  • 5.11 Integration Involving PWL Function
  • Chapter 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
  • 6.4.1 Adams‐Bashforth‐Moulton Method
  • 6.4.2 Hamming Method
  • 6.4.3 Comparison of Methods
  • 6.5 Vector Differential Equations
  • 6.5.1 State Equation
  • 6.5.2 Discretization of LTI State Equation
  • 6.5.3 High‐order Differential Equation to State Equation
  • 6.5.4 Stiff Equation
  • 6.6 Boundary Value Problem (BVP)
  • 6.6.1 Shooting Method
  • 6.6.2 Finite Difference Method
  • Chapter 7 Optimization
  • 7.1 Unconstrained Optimization
  • 7.1.1 Golden Search Method
  • 7.1.2 Quadratic Approximation Method
  • 7.1.3 Nelder‐Mead Method
  • 7.1.4 Steepest Descent Method
  • 7.1.5 Newton Method
  • 7.1.6 Conjugate Gradient Method
  • 7.1.7 Simulated Annealing
  • 7.1.8 Genetic Algorithm
  • 7.2 Constrained Optimization
  • 7.2.1 Lagrange Multiplier Method
  • 7.2.2 Penalty Function Method
  • 7.3 MATLAB Built‐In Functions for Optimization
  • 7.3.1 Unconstrained Optimization
  • 7.3.2 Constrained Optimization
  • 7.3.3 Linear Programming (LP)
  • 7.3.4 Mixed Integer Linear Programming (MILP)
  • 7.4 Neural Network[K‐1]
  • 7.5 Adaptive Filter[Y‐3]
  • 7.6 Recursive Least Square Estimation (RLSE)[Y‐3]
  • Chapter 8 Matrices and Eigenvalues
  • 8.1 Eigenvalues and Eigenvectors
  • 8.2 Similarity Transformation and Diagonalization
  • 8.3 Power Method
  • 8.3.1 Scaled Power Method
  • 8.3.2 Inverse Power Method
  • 8.3.3 Shifted Inverse 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]
  • Chapter 9 Partial Differential Equations
  • 9.1 Elliptic PDE
  • 9.2 Parabolic PDE
  • 9.2.1 The Explicit Forward Euler Method
  • 9.2.2 The Implicit Backward Euler Method.
  • 9.2.3 The Crank‐Nicholson Method
  • 9.2.4 Using the MATLAB function 'pdepe()'
  • 9.2.5 Two‐Dimensional Parabolic PDEs
  • 9.3 Hyperbolic PDES
  • 9.3.1 The Explicit Central Difference Method
  • 9.3.2 Two‐Dimensional Hyperbolic PDEs
  • 9.4 Finite Element Method (FEM) for Solving PDE
  • 9.5 GUI of MATLAB for Solving PDES - PDEtool
  • 9.5.1 Basic PDEs Solvable by PDEtool
  • 9.5.2 The Usage of PDEtool
  • 9.5.3 Examples of Using PDEtool to Solve PDEs
  • Appendix A Mean Value Theorem
  • Appendix B Matrix 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
  • Appendix C Differentiation W.R.T. A Vector
  • Appendix D Laplace Transform
  • Appendix E Fourier Transform
  • Appendix F Useful Formulas
  • Appendix G Symbolic Computation
  • G.1 How to Declare Symbolic Variables and Handle Symbolic Expressions
  • G.2 Calculus
  • G.2.1 Symbolic Summation
  • G.2.2 Limits
  • G.2.3 Differentiation
  • G.2.4 Integration
  • G.2.5 Taylor Series Expansion
  • G.3 Linear Algebra
  • G.4 Solving Algebraic Equations
  • G.5 Solving Differential Equations
  • Appendix H Sparse Matrices
  • Appendix I MATLAB
  • References
  • Index
  • Index for MATLAB Functions
  • Index for Tables
  • EULA.

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