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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This new edition provides an updated approach for students, engineers, and researchers to apply numerical methods for solving problems using MATLAB®
This accessible book makes use of MATLAB® software to teach the fundamental concepts for applying numerical methods to solve practical engineering and/or science problems. It presents programs 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.
Applied Numerical Methods Using MATLAB®, Second Edition begins with an introduction to MATLAB usage and computational errors, covering everything from input/output of data, to various kinds of computing errors, and on to parameter sharing and passing, and more. The system of linear equations is covered next, followed by a chapter on the interpolation by Lagrange polynomial. The next sections look at interpolation and curve fitting, nonlinear equations, numerical differentiation/integration, ordinary differential equations, and optimization. Numerous methods such as the Simpson, Euler, Heun, Runge-kutta, Golden Search, Nelder-Mead, and more are all covered in those chapters. The eighth chapter provides readers with matrices and Eigenvalues and Eigenvectors. The book finishes with a complete overview of differential equations.
- Provides examples and problems of solving electronic circuits and neural networks
- Includes new sections on adaptive filters, recursive least-squares estimation, Bairstow's method for a polynomial equation, and more
- Explains Mixed Integer Linear Programing (MILP) and DOA (Direction of Arrival) estimation with eigenvectors
- Aimed at students who do not like and/or do not have time to derive and prove mathematical results
Applied Numerical Methods Using MATLAB®, Second Edition is an excellent text for students who wish to develop their problem-solving capability without being involved in details about the MATLAB codes. It will also be useful to those who want to delve deeper into understanding underlying algorithms and equations.
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Veröffentlichungsjahr: 2020
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Table of Contents
Cover
Preface
Acknowledgments
About the Companion Website
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
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
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
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
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
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
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]
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]
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
Appendix A: Appendix AMean Value TheoremMean Value Theorem
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
Appendix C: Appendix CDifferentiation W.R.T. A VectorDifferentiation W.R.T. A Vector
Appendix D: Appendix DLaplace TransformLaplace Transform
Appendix E: Appendix EFourier TransformFourier Transform
Appendix F: Appendix FUseful FormulasUseful Formulas
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
Appendix H: Appendix HSparse MatricesSparse Matrices
Appendix I: Appendix IMATLABMATLAB
References
Index
Index for MATLAB Functions
Index for Tables
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Conversion type specifiers and special characters used in fprintf()...
Table 1.2 Graphic line specifications used in the ‘
plot()
’ command.
Table 1.3 Functions and variables inside MATLAB.
Table 1.4 Relational operators and logical operators.
Table P1.4 The depth of the rock layer.
Table P1.16 Results of operations with backslash(
\
) operator and ‘
pinv()
’ c...
Chapter 2
Table 2.1 Residual error and the number of floating‐point operations of vario...
Table P2.2 Comparison of ‘
Gauss()
’ with different pivoting methods in terms o...
Table P2.3 Comparison of several methods for solving a set of linear equation...
Table P2.4 The computational load of the methods to solve a tridiagonal syste...
Table P2.6.1 Comparison of several methods for computing the LS solution.
Table P2.6.2 Comparison of several methods for solving a system of linear equ...
Chapter 3
Table 3.1 Divided difference table.
Table 3.2 Divided differences.
Table 3.3 Chebyshev coefficient polynomials.
Table 3.4 Boundary conditions for a cubic spline.
Table 3.5 Linearization of nonlinear functions by parameter/data transformati...
Table P3.6 Bulirsch‐Stoer method for rational function interpolation.
Chapter 4
Tabe P4.6 Comparison of various methods used for solving nonlinear equations.
Table P4.8 Using ‘Newtons()’/‘fsolve()’ for systems of nonlinear equations.
Table P4.9 Using ‘Newtons()’/‘fsolve()’ for systems of nonlinear equations.
Chapter 5
Table 5.1.1 The forward difference approximation (5.1.4) for the first deriva...
Table 5.1.2 The central difference approximation (5.1.8) for the first deriva...
Table 5.2 The difference approximation formulas for the first and second deri...
Table 5.3 Romberg table.
Table P5.2 Three functions each given as a set of five data pairs.
Table P5.4 Results of using various numerical integration methods.
Table 5.7 Results of using various numerical integration methods for improper...
Table P5.8 Results of using various numerical integration methods.
Table P5.10 Relative error results of suing various numerical integration met...
Table P5.12 Results of using various numerical integration methods for (P5.12...
Table P5.15.1 Results of using ‘
int2s()
’ and “
dblquad()
' for the integral (...
Table P5.15.2 Results of using ‘
int2s()
’ and ‘
dblquad()
’ for the integral (...
Table P5.15.3 Results of using the double integration routine ‘
int2s()
’ for (...
Chapter 6
Table 6.1 A numerical solution of the DE (6.1.1) obtained by the Euler's meth...
Table 6.2 Results of applying several functions for solving a simple DE.
Table P6.11 Comparison of the BVP solvers ‘
bvp2_shoot()
’ and ‘
bvp2_fdf()
’....
Table P6.12 Comparison of the BVP solvers ‘
bvp2_shoot()
’ and ‘
bvp2_fdf()
’....
Chapter 7
Table 7.1 Results of using the several optimization functions with various in...
Table 7.2 Results of using several unconstrained optimization functions with ...
Table 7.3 The names of the MATLAB built‐in minimization functions.
Table P7.2.1 Extrema (maxima/minima) and saddle points of the function (P7.2....
Table P7.2.2 Points reached by the several optimization functions.
Table P7.7 The results of using ‘
fmincon()
’ with different initial guess.
Table P7.8 The results of penalty methods depending on the initial guess and ...
Chapter 9
Table P9.8.1 The maximum absolute error and the number of nodes.
Table P9.8.2 The maximum absolute error and the number of nodes.
Table P9.8.3 The maximum absolute error and the number of nodes.
4
Table D.1
Laplace transforms of basic functions.
Table D.2
Properties of Laplace transform.
5
Table E.1
Definition and properties of the CTFT (continuous‐time Fourier transfo...
Table E.2
Properties of DTFT (discrete‐time Fourier transform.)
9
Table I.1 Some frequently used MATLAB commands.
Table I.2 Graphic line specifications used in the
plot()
command.
Table I.3 Functions and variables in MATLAB.
List of Illustrations
Chapter 1
Figure 1.1 Plot of a 5 × 2 matrix data representing the variations of the hi...
Figure 1.2 Examples of graphs obtained using the ‘
plot()
’ command. (a) Dat...
Figure 1.3 Graphs drawn by using various graphic commands.
Figure 1.4 3D graphs drawn by using
plot3()
,
mesh()
, and
contour()
.
Figure 1.5 Distribution (histogram) of noise generated by the
rand()
/
ran
...
Figure 1.6 Process of adding two numbers, 3 and 14, in MATLAB.
Figure 1.7 Graphs of sinc functions. Using ‘
sinc1()
’ without division‐by‐z...
Figure P1.5 Plotting the graph of
f
(
x
) = tan
x
.
Figure P1.10 The characteristic of an analog‐to‐digital converter (ADC).
Figure P1.13 The graph of piece‐wise polynomial functions.
Figure P1.20 Process of addition/subtraction with four mantissa bits.
Figure P1.28 Graphs for Problem 1.28. (a1) A rectangular pulse function
r
D
(
t
Chapter 2
Figure 2.1 A minimum‐norm solution.
Figure 2.2 Graphs for Eqs. (E2.6.1a,b).
Chapter 3
Figure 3.1 The graph of a third‐degree Lagrange polynomial.
Figure 3.2 Interpolation from the viewpoint of approximation. (a) 4/8/10th‐D...
Figure 3.3 Chebyshev nodes (with
N
= 4). (a) 4/8/10th‐degree polynomial appr...
Figure 3.4 Approximation using the Chebyshev polynomial.
Figure 3.5 Chebyshev polynomial functions. (a)
T
0
(
x
′) = 1, (b)
T
0
(
x
′) =
x
′, ...
Figure 3.6 Pade approximation and Taylor series expansion for
f
(
x
) =
e
x
(Exa...
Figure 3.7 Cubic splines for Example 3.3.
Figure 3.8 2D interpolation using
Zi=interp2()
on the grid array gener...
Figure 3.9 Two‐dimensional approximation (Example 3.5). (a) True function, (...
Figure 3.10 Polynomial curve fitting by the LS method. (a) Approximating pol...
Figure 3.11 LS curve fitting and WLS curve fitting for Example 3.7. (a) Fitt...
Figure 3.12 Using ‘cftool’ for curve fitting.
Figure 3.13 The DFT(FFT) {
X(k), k = 0 : N − 1
...
Figure 3.14 DFT spectra of a two‐tone signal. (a) polar(th,
r
), (b) semilog
x
(
Figure 3.15 Interpolation/smoothing using DFS/DFT. (a) Original discrete‐tim...
Figure P3.4 Chebyshev nodes.
Figure P3.9 Coordinates and path of a robot planned using the cubic spline. ...
Figure P3.11 LS fitting curves for data pairs with various relations.
Figure P3.15 LS and WLS fitting curves to
y
=
axe
bx
.
Figure P3.17.1 Two rectangular pulses, a triangular pulse, and a dual triang...
Figure P3.17.2 Effects of sampling period, zero‐padding, and whole interval ...
Figure P3.18 The effect of windowing on DFT spectrum. (a) Rectangular window...
Chapter 4
Figure 4.1 Chebyshev nodes. (a)
. (b)
.
Figure 4.2 Bisection method for Example 4.2. (a) Graphic description of the ...
Figure 4.3 False position method for solving
f
(
x
) = tan(
π
−
x
) −
x
.
Figure 4.4 Solving nonlinear equations
f
(
x
) = 0 using the Newton method. (a)...
Figure 4.5 Secant method for solving
f
(
x
) = tan(
π
−
x
) −
x
.
Figure 4.6 Solving nonlinear equations
f
(
x
) = 0 using the Newton method. (a)...
Figure 4.7 Solving nonlinear equations
f
(
x
) = 0 using the Newton method.
Figure 4.8 A BJT circuit and its PSpice schematic with DC (bias point) analy...
Figure 4.9 A complementary BJT circuit and its PSpice schematic. (a) A compl...
Figure P4.1 Fixed‐point iteration for solving
f
(
x
) =
x
2
− 3
x
+ 1 = 0. (a)
....
Figure P4.3 Bisection method for solving
f
(
x
) = tan(
π
−
x
) −
x
= 0.
Figure P4.10 A BJT circuit and its PSpice simulation results with DC (bias p...
Figure P4.11 A BJT circuit (a) and its PSpice schematic with DC (bias point)...
Figure P4.12 An NMOS circuit (a) and its PSpice schematic with DC (bias poin...
Figure P4.14 Single‐stub impedance matching.
Figure P4.15 Two‐port networks in cascade interconnection.
Chapter 5
Figure 5.1 Forward/central difference approximation error of the first deriv...
Figure 5.2 Forward/central difference approximation error of the first deriv...
Figure 5.3 Various methods of numerical integration using Newton–Cotes rules...
Figure 5.4 Subintervals (segments) and their boundary points (nodes) determi...
Figure 5.5 Region for a double integral.
Figure 5.6 One‐fourth (1/4) of a unit sphere (with the radius of 1).
Figure 5.7 A piecewise linear (PWL) waveform.
Figure 5.8 A piecewise linear (PWL) waveform.
Figure P5.5 The graph of the integrand function of the integral (P5.5.1)
Figure P5.11 Bit error rate (BER) vs. SNR curves for multidimensional (ortho...
Figure P5.14 A unit sphere.
Chapter 6
Figure 6.1 Numerical solutions of the DE
y′
(
t
) +
y
(
t
) = 1 with
y
(0) = ...
Figure 6.2 Numerical solutions of the DE
y
′(
t
) +
y
(
t
) = 1 with
y
(0) = 0.
Figure 6.3 Numerical solutions and their errors for the DE
y
′(
t
) = −
y
(
t
) + 1...
Figure 6.4 Numerical solutions and their errors for the DE
y
′(
t
) =
y
(
t
) + 1....
Figure 6.5 Numerical/analytical solutions of the state equation (6.5.2)/(6.5...
Figure 6.6 Solutions of the discretized state equation (6.5.21).
Figure 6.7 Solution graphs for Example 6.1. (a) Numerical solution using
o
...
Figure 6.8 Solution graphs for Example 6.2. (a) Numerical solution using
o
...
Figure 6.9 The solution of the BVP (6.1) obtained by using the shooting meth...
Figure 6.10 The solution of the BVP (6.1) obtained by using the finite diffe...
Figure P6.1.1 Contours and gradient vectors for a function of two variables
Figure P6.1.2 A surface and its normal vectors each plotted using ‘surf()’ a...
Figure P6.1.3 Slope/direction fields and possible solutions for differential...
Figure P6.4.1 Block diagram of a PLL circuit.
Figure P6.4.2 A DC motor system.
Figure P6.4.3 A two‐mesh
RC
circuit.
Figure P6.5 A model for vehicle suspension system. (a) The block diagram and...
Figure P6.6 The paths of a satellite with the same initial position and diff...
Figure P6.7 The output voltages of an
RC
diode circuit obtained from PSpice ...
Figure P6.13 Solutions of eigenvalue BVPs.
Chapter 7
Figure 7.1 Illustration of the golden search method.
Figure 7.2 Illustration of the quadratic approximation method.
Figure 7.3 Illustration of the Nelder–Mead method. (a) Notations used in the...
Figure 7.4 Illustration of the Newton's method and steepest descent method....
Figure 7.5 Illustration of the conjugate gradient method.
Figure 7.6 Some illustrative functions used for controlling the randomness –...
Figure 7.7 Flowchart of genetic algorithm (GA).
Figure 7.8 Reproduction/crossover/mutation in one iteration of genetic algor...
Figure 7.9 The objective and constraint functions for Example 7.1. (a) Mesh‐...
Figure 7.10 The objective and constraint functions for Example 7.3.
Figure 7.11 The objective and constraint functions for Example 7.4. (a) Mesh...
Figure 7.12 Minimum points in the admissible region (satisfying the constrai...
Figure 7.13 The contours, local minima/maxima, and saddle points of the obje...
Figure 7.14 The result of using the MATLAB built‐in function ‘lsqnonlin()’ f...
Figure 7.15 Illustration of the Newton's method and steepest descent method....
Figure 7.16 The objective function, constraints, and solution of an LP probl...
Figure 7.17 The objective function, constraints, and solution of an ILP prob...
Figure 7.18 Branch‐and‐bound (BB) search (enumeration) tree for finding the ...
Figure 7.19 A neural network (NN) with supervised learning scheme.
Figure 7.20 Error reducing as the training process goes on.
Figure 7.21 An FIR filter.
Figure 7.22 Updating the parameter of an adaptive predictor using the steepe...
Figure 7.23 LMS and RLS adaptive parameter estimation. (a) Parameter estimat...
Figure P7.2 The contour, extrema, and saddle points of the objective functio...
Figure P7.3 The graph of
f(x) = sin(1/x)/{(x − 0.2)2 + 0.1}
...
Figure P7.4 The contour for the objective function (P7.4.1) and lines showin...
Figure P7.10 The site of a new warehouse and the locations factories.
Figure P7.11 Refraction of a light ray at an air‐glass interface.
Figure P7.13 Two objective functions for training a neural network. (a)
J
a
=...
Chapter 8
Figure 8.1 Three basis vectors obtained using the Gram‐Schmidt orthogonaliza...
Figure 8.2 Eigenvectors and eigenvalues of a covariance matrix.
Figure 8.3 Eigenvectors and eigenvalues of a covariance matrix.
Figure 8.4 An undamped mass–spring system.
Figure 8.5 Solutions for Example 8.6 (results obtained by running the script...
Figure 8.6 An
N
e
= 4‐element UCA receiving two signals
s
1
(
n
) and
s
2
(
n
).
Figure 8.7 Spatial spectra and reconstructed signals. (a1) Spatial spectrum
Figure P8.5 Householder reflection.
Chapter 9
Figure 9.1 Grid for an elliptic PDE with Dirichlet/Neumann boundary conditio...
Figure 9.2 Temperature distribution over a rectangular plate for Example 9.1...
Figure 9.3 Results of various algorithms for a 1D parabolic PDE – heat equat...
Figure 9.4 Temperature distribution over a plate for Example 9.3.
Figure 9.5 Solution to the 1D hyperbolic PDE for Example 9.4. (a) The soluti...
Figure 9.6 Solution to the 2D hyperbolic PDE – vibration of a square membran...
Figure 9.7 A region (domain) divided into four triangular subregions.
Figure 9.8 The basis (shape) functions for nodes in Figure 9.7 and a composi...
Figure 9.9 An example of triangular subregions for FEM.
Figure 9.10 FEM solutions for Example 9.6. (a) 31‐point FEM (finite element ...
Figure 9.11 The GUI (graphical user interface) window of the MATLAB PDEtool....
Figure 9.12 Pull‐down menus from the top menu and its submenu of the MATLAB ...
Figure 9.13 Using PDEtool Example 9.1/9.7. (a) Specifying the BCs for the do...
Figure 9.14 Using PDEtool Example 9.3/9.8. (a) PDE Specification dialog box....
Figure 9.15 Using PDEtool Example 9.5/9.9. (a) PDE Specification dialog box....
Figure 9.16 Using PDEtool Example 9.6/9.10. (a) PDE Specification dialog box...
Figure P9.7 Refined triangular meshes for Problem 9.7.
1
Figure A.1 Mean value theorem.
9
Figure I.1 The MATLAB desktop with Command/Editor/Current folder/Workspace w...
Figure I.2 The MATLAB desktop with Command/Editor/Current folder/Workspace w...
Guide
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Applied Numerical Methods Using MATLAB®
Second Edition
Won Y. Yang
Wenwu Cao
Jaekwon Kim
Kyung W. Park
Ho‐Hyun Park
Jingon Joung
Jong‐Suk Ro
Han L. Lee
Cheol‐Ho Hong
Taeho Im
This edition first published 2020
© 2020 John Wiley & Sons, Inc
Edition History
Wiley‐Interscience (1e 2005)
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The right of Won Y. Yang, Wenwu Cao, Jaekwon Kim, Kyung W. Park, Ho‐Hyun Park, Jingon Joung, Jong‐Suk Ro, Han L. Lee, Cheol‐Ho Hong, Taeho Im to be identified as the authors of this work has been asserted in accordance with law.
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Limit of Liability/Disclaimer of Warranty
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This work's use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
Library of Congress Cataloging‐in‐Publication Data
Names: Yang, Won Y., 1953- author. | Cao, Wenwu, author. | Kim,
Jaekwon, 1972- author. | Park, Kyung W., 1976- author. | Park, Ho Hyun,
1964- author. | Joung, Jingon, 1974- author. | Ro, Jong Suk, 1975-
author. | Lee, Han L., 1983- author. | Hong, Cheol Ho, 1977- author. |
Im, Taeho, 1979- author.
Title: Applied numerical methods using MATLAB® / Won Y. Yang, Wenwu Cao,
Jaekwon Kim, Kyung W. Park, Ho Hyun Park, Jingon Joung, Jong Suk Ro, Han
L. Lee, Cheol Ho Hong, Taeho Im.
Description: Second edition. | Hoboken, NJ : Wiley, 2020. | Includes
bibliographical references and index.
Identifiers: LCCN 2019030074 (print) | LCCN 2019030075 (ebook) | ISBN
9781119626800 (hardback) | ISBN 9781119626718 (adobe pdf) | ISBN
9781119626824 (epub)
Subjects: LCSH: MATLAB. | Numerical analysis--Data processing.
Classification: LCC QA297 .A685 2020 (print) | LCC QA297 (ebook) | DDC
518--dc23
LC record available at https://lccn.loc.gov/2019030074
LC ebook record available at https://lccn.loc.gov/2019030075
Cover Design: Wiley
Cover Image: © Yurchanka Siarhei/Shutterstock
To our parents and families who love and support us and to our teachers and students who enriched our knowledge
Preface
This book introduces applied numerical methods for engineering and science students in sophomore to senior levels; it targets the students of today who do not like and/or do not have time to derive and prove mathematical results. It can also serve as a reference to MATLAB applications for professional engineers and scientists, since many of the MATLAB codes presented after introducing each algorithm's basic ideas can easily be modified to solve similar problems even by those who do not know what is going on inside the MATLAB routines and the algorithms they use. Just as most drivers have to know only where to go and how to drive a car to get to their destinations, most users have to know only how to formulate their problems that they want to solve using MATLAB and how to use the corresponding routines for solving them. We never deny that detailed knowledge about the algorithm (engine) of the program (car) is helpful for getting safely to the solution (destination); we only imply that one‐time users of any MATLAB program or routine may use this book as well as the readers who want to understand the underlying principle/equations of each algorithm.
This book mainly focuses on helping readers understand the fundamental mathematical concepts and practice problem‐solving skills using MATLAB‐based numerical methods, skipping some tedious derivations/proofs. Obviously, basic concepts must be taught so that readers can properly formulate the mathematics problems. Afterward, readers can directly use the MATLAB codes to solve practical problems. Almost every algorithm introduced in this book is followed by example MATLAB code with a friendly interface so that students can easily modify the code to solve their own problems. The selection of exercises follows the same philosophy of making the learning easy and practical. Readers should be able to solve similar problems immediately after reading the materials and codes listed in this book. For most students – and particularly non‐math majors – understanding how to use numerical tools correctly in solving their problems of interest is more important than doing lengthy proofs and derivations.
MATLAB is one of the most developed software packages available today. It provides many numerical methods and it is very easy to use, even for those having no programming technique or experience. We have supplemented MATLAB's built‐in functions with over 100 small MATLAB routines. Readers should find these routines handy and useful. Some of these routines give better results for some problems than the built‐in functions. Readers are encouraged to develop their own routines following the examples.
Compared with the first edition, Bairstow's method (Section 4.7), Integration Involving PWL Function (Section 5.11), Mixed Integer Linear Programming (Section 7.3.4), Neural Network (Section 7.4), Adaptive Filter (Section 7.5), Recursive Least‐Squares Estimation (Section 7.6), and DoA Estimation (Section 8.8) have been added to the second edition.
Program files can be downloaded from <https://wyyang53.wixsite.com/mysite/publications>. Any questions, comments, and suggestions regarding this book are welcome and they should be mailed to [email protected].
Won Y. Yang et al.
March 2020
Acknowledgments
The knowledge in this book is derived from the work of many eminent scientists, scholars, researchers, and MATLAB developers, all of whom we thank. We thank our colleagues, students, relatives, and friends for their support and encouragement. We thank the reviewers, whose comments were so helpful in tuning this book. We gratefully acknowledge the editorial, Brett Kurzman and production staff of John Wiley & Sons, Inc. including Project Editor Antony Sami and Production Editor Gayathree Sekar for their kind, efficient, and encouraging guide.
About the Companion Website
Don't forget to visit the companion website for this book:
www.wiley.com/go/yang/appliednumericalmethods
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There you will find valuable material designed to enhance your learning, including:
Learning Outcomes for all chapters
Exercises for all chapters
References for all chapters
Further reading for all chapters
Figures for chapters 16, 22 and 30
