Applied Numerical Methods Using MATLAB.

Format:

Book

Author/Creator:

Yang, Wŏn-yŏng, 1953-

Contributor:

Cao, Wenwu.

Kim, Jaekwon.

Park, Kyung W.

Park, Ho-Hyun.

Joung, Jingon.

Ro, Jong-Suk.

Lee, Han L.

Hong, Cheol-Ho.

Im, Taeho.

Language:

English

Subjects (All):

MATLAB.

Numerical analysis--Data processing.

Numerical analysis.

Physical Description:

1 online resource (653 pages)

Edition:

2nd ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2020.

Summary:

"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 understanding the mathematical manipulation process and making interpretations of the results. The book targets students who do not like and/or do not have time to derive and prove mathematical results, helping them develop their problem-solving capability without being involved in details about the MATLAB codes. It also targets students who want to delve into details, helping them understand underlying algorithms and equations as deeply as they want"-- Provided by publisher.

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9781523155095

1523155094

9781119626824

111962682X

9781119626879

1119626870

9781119626718

1119626714

OCLC:

1128890321