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E-grāmata: Scientific Computing with MATLAB

(University of California, Merced, USA), (Northeastern University, Shenyang, China)
  • Formāts: 604 pages
  • Izdošanas datums: 03-Sep-2018
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781315362106
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Scientific Computing with MATLABPalielināt
  • Formāts: 604 pages
  • Izdošanas datums: 03-Sep-2018
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781315362106
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Scientific Computing with MATLAB®, Second Edition improves students ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter.

The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

Recenzijas

Praise for the First Edition:" this volume has many interesting cases to illustrate the power of MATLAB." Bulletin of the Belgian Mathematical Society, Volume 20, 2013

"The readers ability to tackle mathematical problems can be significantly enhanced after reading this book. This book can be used as a reference text for almost all college students, both undergraduates and graduates, in almost all disciplines that require certain levels of applied mathematics. This book will be a good desktop reference for many who have graduated from college and are still involved in solving mathematical problems in their jobs. A lot of MATLAB function designed by the authors and some third-party free toolboxes are also presented in the book." Zentralblatt MATH, 1156

Preface xiii
Preface of the First Edition xv
1 Computer Mathematics Languages - An Overview 1(14)
1.1 Computer Solutions to Mathematics Problems
1(7)
1.1.1 Why should we study computer mathematics language?
1(4)
1.1.2 Analytical solutions versus numerical solutions
5(1)
1.1.3 Mathematics software packages: an overview
5(1)
1.1.4 Limitations of conventional computer languages
6(2)
1.2 Summary of Computer Mathematics Languages
8(1)
1.2.1 A brief historic review of MATLAB
8(1)
1.2.2 Three widely used computer mathematics languages
8(1)
1.2.3 Introduction to free scientific open-source softwares
9(1)
1.3 Outline of the Book
9(4)
1.3.1 The organization of the book
9(2)
1.3.2 How to learn and use MATLAB
11(1)
1.3.3 The three-phase solution methodology
11(2)
Exercises
13(1)
Bibliography
13(2)
2 Fundamentals of MATLAB Programming and Scientific Visualization 15(46)
2.1 Essentials in MATLAB Programming
16(4)
2.1.1 Variables and constants in MATLAB
16(1)
2.1.2 Data structures
16(2)
2.1.3 Basic statement structures of MATLAB
18(1)
2.1.4 Colon expressions and sub-matrices extraction
19(1)
2.2 Fundamental Mathematical Calculations
20(5)
2.2.1 Algebraic operations of matrices
20(2)
2.2.2 Logic operations of matrices
22(1)
2.2.3 Relationship operations of matrices
22(1)
2.2.4 Simplifications and presentations of analytical results
22(2)
2.2.5 Basic number theory computations
24(1)
2.3 Flow Control Structures of MATLAB Language
25(5)
2.3.1 Loop control structures
26(1)
2.3.2 Conditional control structures
27(1)
2.3.3 Switch structure
28(1)
2.3.4 Trial structure
29(1)
2.4 Writing and Debugging MATLAB Functions
30(5)
2.4.1 Basic structure of MATLAB functions
30(3)
2.4.2 Programming of functions with variable numbers of arguments in inputs and outputs
33(1)
2.4.3 Inline functions and anonymous functions
34(1)
2.4.4 Pseudo code and source code protection
34(1)
2.5 Two-dimensional Graphics
35(9)
2.5.1 Basic statements of two-dimensional plotting
35(2)
2.5.2 Plotting with multiple horizontal or vertical axes
37(1)
2.5.3 Other two-dimensional plotting functions
38(1)
2.5.4 Plots of implicit functions
39(1)
2.5.5 Graphics decorations
40(2)
2.5.6 Data file access with MATLAB
42(2)
2.6 Three-dimensional Graphics
44(9)
2.6.1 Plotting of three-dimensional curves
44(1)
2.6.2 Plotting of three-dimensional surfaces
45(3)
2.6.3 Viewpoint settings in 3D graphs
48(1)
2.6.4 Surface plots of parametric equations
49(1)
2.6.5 Spheres and cylinders
50(1)
2.6.6 Drawing 2D and 3D contours
51(1)
2.6.7 Drawing 3D implicit functions
52(1)
2.7 Four-dimensional Visualization
53(2)
Exercises
55(5)
Bibliography
60(1)
3 Calculus Problems 61(60)
3.1 Analytical Solutions to Limit Problems
61(6)
3.1.1 Limits of univariate functions
62(2)
3.1.2 Limits of interval functions
64(2)
3.1.3 Limits of multivariate functions
66(1)
3.2 Analytical Solutions to Derivative Problems
67(8)
3.2.1 Derivatives and high-order derivatives
67(2)
3.2.2 Partial derivatives of multivariate functions
69(2)
3.2.3 Jacobian matrix of multivariate functions
71(1)
3.2.4 Hessian partial derivative matrix
72(1)
3.2.5 Partial derivatives of implicit functions
72(2)
3.2.6 Derivatives of parametric equations
74(1)
3.2.7 Gradients, divergences and curls of fields
74(1)
3.3 Analytical Solutions to Integral Problems
75(5)
3.3.1 Indefinite integrals
76(1)
3.3.2 Computing definite, infinite and improper integrals
77(2)
3.3.3 Computing multiple Integrals
79(1)
3.4 Series Expansions and Finite-term Series Approximations
80(6)
3.4.1 Taylor series expansion
80(3)
3.4.2 Fourier series expansion
83(3)
3.5 Infinite Series and Products
86(5)
3.5.1 Series
87(1)
3.5.2 Product of sequences
88(1)
3.5.3 Convergence test of infinite series
89(2)
3.6 Path Integrals and Line Integrals
91(3)
3.6.1 Path integrals
91(2)
3.6.2 Line integrals
93(1)
3.7 Surface Integrals
94(3)
3.7.1 Scalar surface integrals
94(2)
3.7.2 Vector surface integrals
96(1)
3.8 Numerical Differentiation
97(4)
3.8.1 Numerical differentiation algorithms
97(1)
3.8.2 Central-point difference algorithm with MATLAB implementation
98(2)
3.8.3 Gradient computations of functions with two variables
100(1)
3.9 Numerical Integration Problems
101(12)
3.9.1 Numerical integration from given data using trapezoidal method
102(1)
3.9.2 Numerical integration of univariate functions
103(3)
3.9.3 Numerical infinite integrals
106(1)
3.9.4 Evaluating integral functions
107(1)
3.9.5 Numerical solutions to double integrals
108(3)
3.9.6 Numerical solutions to triple integrals
111(1)
3.9.7 Multiple integral evaluations
112(1)
Exercises
113(6)
Bibliography
119(2)
4 Linear Algebra Problems 121(62)
4.1 Inputting Special Matrices
122(6)
4.1.1 Numerical matrix input
122(4)
4.1.2 Defining symbolic matrices
126(1)
4.1.3 Sparse matrix input
127(1)
4.2 Fundamental Matrix Operations
128(14)
4.2.1 Basic concepts and properties of matrices
128(7)
4.2.2 Matrix inversion
135(3)
4.2.3 Generalized matrix inverse
138(2)
4.2.4 Matrix eigenvalue problems
140(2)
4.3 Fundamental Matrix Transformations
142(13)
4.3.1 Similarity transformations and orthogonal matrices
142(2)
4.3.2 Triangular and Cholesky factorizations
144(5)
4.3.3 Companion, diagonal and Jordan transformations
149(3)
4.3.4 Singular value decompositions
152(3)
4.4 Solving Matrix Equations
155(11)
4.4.1 Solutions to linear algebraic equations
155(3)
4.4.2 Solutions to Lyapunov equations
158(3)
4.4.3 Solutions to Sylvester equations
161(2)
4.4.4 Solutions of Diophantine equations
163(2)
4.4.5 Solutions to Riccati equations
165(1)
4.5 Nonlinear Functions and Matrix Function Evaluations
166(9)
4.5.1 Element-by-element computations
166(1)
4.5.2 Computations of matrix exponentials
166(2)
4.5.3 Trigonometric functions of matrices
168(3)
4.5.4 General matrix functions
171(2)
4.5.5 Power of a matrix
173(2)
Exercises
175(5)
Bibliography
180(3)
5 Integral Transforms and Complex-valued Functions 183(48)
5.1 Laplace Transforms and Their Inverses
184(6)
5.1.1 Definitions and properties
184(1)
5.1.2 Computer solution to Laplace transform problems
185(2)
5.1.3 Numerical solutions of Laplace transforms
187(3)
5.2 Fourier Transforms and Their Inverses
190(7)
5.2.1 Definitions and properties
190(1)
5.2.2 Solving Fourier transform problems
191(2)
5.2.3 Fourier sinusoidal and cosine transforms
193(1)
5.2.4 Discrete Fourier sine, cosine transforms
194(1)
5.2.5 Fast Fourier transforms
195(2)
5.3 Other Integral Trasforms
197(3)
5.3.1 Mellin transform
197(1)
5.3.2 Hankel transform solutions
198(2)
5.4 z Transforms and Their Inverses
200(3)
5.4.1 Definitions and properties of z transforms and inverses
200(1)
5.4.2 Computations of z transform
201(1)
5.4.3 Bilateral z transforms
202(1)
5.4.4 Numerical inverse z transform of rational functions
203(1)
5.5 Essentials of Complex-valued Functions
203(4)
5.5.1 Complex matrices and their manipulations
204(1)
5.5.2 Mapping of complex-valued functions
204(2)
5.5.3 Riemann surfaces
206(1)
5.6 Solving Complex-valued Function Problems
207(14)
5.6.1 Concept and computation of poles and residues
207(3)
5.6.2 Partial fraction expansion for rational functions
210(4)
5.6.3 Inverse Laplace transform using PFEs
214(1)
5.6.4 Laurent series expansions
215(4)
5.6.5 Computing closed-path integrals
219(2)
5.7 Solutions of Difference Equations
221(5)
5.7.1 Analytical solutions of linear difference equations
221(1)
5.7.2 Numerical solutions of linear time varying difference equations
222(2)
5.7.3 Solutions of linear time-invariant difference equations
224(1)
5.7.4 Numerical solutions of nonlinear difference equations
225(1)
Exercises
226(4)
Bibliography
230(1)
6 Nonlinear Equations and Numerical Optimization Problems 231(74)
6.1 Nonlinear Algebraic Equations
232(8)
6.1.1 Graphical method for solving nonlinear equations
232(2)
6.1.2 Quasi-analytic solutions to polynomial-type equations
234(4)
6.1.3 Numerical solutions to general nonlinear equations
238(2)
6.2 Nonlinear Equations with Multiple Solutions
240(8)
6.2.1 Numerical solutions
241(4)
6.2.2 Finding high-precision solutions
245(2)
6.2.3 Solutions of underdetermined equations
247(1)
6.3 Unconstrained Optimization Problems
248(9)
6.3.1 Analytical solutions and graphical solution methods
249(1)
6.3.2 Solution of unconstrained optimization using MATLAB
250(2)
6.3.3 Global minimum and local minima
252(3)
6.3.4 Solving optimization problems with gradient information
255(2)
6.4 Constrained Optimization Problems
257(11)
6.4.1 Constraints and feasibility regions
257(1)
6.4.2 Solving linear programming problems
258(5)
6.4.3 Solving quadratic programming problems
263(1)
6.4.4 Solving general nonlinear programming problems
264(4)
6.5 Mixed Integer Programming Problems
268(8)
6.5.1 Enumerate method in integer programming problems
268(2)
6.5.2 Solutions of linear integer programming problems
270(1)
6.5.3 Solutions of nonlinear integer programming problems
271(2)
6.5.4 Solving binary programming problems
273(2)
6.5.5 Assignment problems
275(1)
6.6 Linear Matrix Inequalities
276(7)
6.6.1 A general introduction to LMIs
276(1)
6.6.2 Lyapunov inequalities
277(2)
6.6.3 Classification of LMI problems
279(1)
6.6.4 LMI problem solutions with MATLAB
279(2)
6.6.5 Optimization of LMI problems by YALMIP Toolbox
281(2)
6.7 Solutions of Multi-objective Programming Problems
283(8)
6.7.1 Multi-objective optimization model
283(1)
6.7.2 Least squares solutions of unconstrained multi-objective programming problems
283(1)
6.7.3 Converting multi-objective problems into single-objective ones
284(3)
6.7.4 Pareto front of multi-objective programming problems
287(2)
6.7.5 Solutions of minimax problems
289(1)
6.7.6 Solutions of multi-objective goal attainment problems
290(1)
6.8 Dynamic Programming and Shortest Path Planning
291(6)
6.8.1 Matrix representation of graphs
292(1)
6.8.2 Optimal path planning of oriented graphs
292(4)
6.8.3 Optimal path planning of undigraphs
296(1)
6.8.4 Optimal path planning for graphs described by coordinates
296(1)
Exercises
297(6)
Bibliography
303(2)
7 Differential Equation Problems 305(76)
7.1 Analytical Solution Methods for Some Ordinary Differential Equations
306(6)
7.1.1 Linear time-invariant ordinary differential equations
306(1)
7.1.2 Analytical solution with MATLAB
307(3)
7.1.3 Analytical solutions of linear state space equations
310(1)
7.1.4 Analytical solutions to special nonlinear differential equations.
311(1)
7.2 Numerical Solutions to Ordinary Differential Equations
312(8)
7.2.1 Overview of numerical solution algorithms
312(2)
7.2.2 Fixed-step Runge-Kutta algorithm and its MATLAB implementation
314(1)
7.2.3 Numerical solution to first-order vector ODEs
315(5)
7.3 Transforms to Standard Differential Equations
320(8)
7.3.1 Manipulating a single high-order ODE
320(1)
7.3.2 Manipulating multiple high-order ODEs
321(4)
7.3.3 Validation of numerical solutions to ODEs
325(1)
7.3.4 Transformation of differential matrix equations
326(2)
7.4 Solutions to Special Ordinary Differential Equations
328(14)
7.4.1 Solutions of stiff ordinary differential equations
329(3)
7.4.2 Solutions of implicit differential equations
332(3)
7.4.3 Solutions to differential algebraic equations
335(2)
7.4.4 Solutions of switching differential equations
337(1)
7.4.5 Solutions to linear stochastic differential equations
338(4)
7.5 Solutions to Delay Differential Equations
342(6)
7.5.1 Solutions of typical delay differential equations
342(2)
7.5.2 Solutions of differential equations with variable delays
344(3)
7.5.3 Solutions of neutral-type delay differential equations
347(1)
7.6 Solving Boundary Value Problems
348(7)
7.6.1 Shooting algorithm for linear equations
348(2)
7.6.2 Boundary value problems of nonlinear equations
350(2)
7.6.3 Solutions to general boundary value problems
352(3)
7.7 Introduction to Partial Differential Equations
355(10)
7.7.1 Solving a set of one-dimensional partial differential equations
355(2)
7.7.2 Mathematical description to two-dimensional PDEs
357(1)
7.7.3 The GUI for the PDE Toolbox - an introduction
358(7)
7.8 Solving ODEs with Block Diagrams in Simulink
365(8)
7.8.1 A brief introduction to Simulink
365(1)
7.8.2 Simulink - relevant blocks
365(2)
7.8.3 Using Simulink for modeling and simulation of ODEs
367(6)
Exercises
373(6)
Bibliography
379(2)
8 Data Interpolation and Functional Approximation Problems 381(56)
8.1 Interpolation and Data Fitting
382(12)
8.1.1 One-dimensional data interpolation
382(3)
8.1.2 Definite integral evaluation from given samples
385(2)
8.1.3 Two-dimensional grid data interpolation
387(2)
8.1.4 Two-dimensional scattered data interpolation
389(3)
8.1.5 Optimization problems based on scattered sample data
392(1)
8.1.6 High-dimensional data interpolations
393(1)
8.2 Spline Interpolation and Numerical Calculus
394(7)
8.2.1 Spline interpolation in MATLAB
395(3)
8.2.2 Numerical differentiation and integration with splines
398(3)
8.3 Fitting Mathematical Models from Data
401(7)
8.3.1 Polynomial fitting
401(2)
8.3.2 Curve fitting by linear combination of basis functions
403(2)
8.3.3 Least squares curve fitting
405(2)
8.3.4 Least squares fitting of multivariate functions
407(1)
8.4 Rational Function Approximations
408(8)
8.4.1 Approximation by continued fraction expansions
408(4)
8.4.2 Pade rational approximations
412(2)
8.4.3 Special approximation polynomials
414(2)
8.5 Special Functions and Their Plots
416(9)
8.5.1 Gamma functions
416(2)
8.5.2 Beta functions
418(1)
8.5.3 Legendre functions
419(1)
8.5.4 Bessel functions
420(1)
8.5.5 Mittag-Leffler functions
421(4)
8.6 Signal Analysis and Digital Signal Processing
425(8)
8.6.1 Correlation analysis
425(2)
8.6.2 Power spectral analysis
427(2)
8.6.3 Filtering techniques and filter design
429(4)
Exercises
433(3)
Bibliography
436(1)
9 Probability and Mathematical Statistics Problems 437(48)
9.1 Probability Distributions and Pseudorandom Numbers
438(10)
9.1.1 Introduction to probability density functions and cumulative distribution functions
438(1)
9.1.2 Probability density functions and cumulative distribution functions of commonly used distributions
439(8)
9.1.3 Random numbers and pseudorandom numbers
447(1)
9.2 Solving Probability Problems
448(6)
9.2.1 Histogram and pie representation of discrete numbers
448(2)
9.2.2 Probability computation of continuous functions
450(1)
9.2.3 Monte Carlo solutions to mathematical problems
451(2)
9.2.4 Simulation of random walk processes
453(1)
9.3 Fundamental Statistical Analysis
454(8)
9.3.1 Mean and variance of stochastic variables
454(2)
9.3.2 Moments of stochastic variables
456(1)
9.3.3 Covariance analysis of multivariate stochastic variables
457(1)
9.3.4 Joint PDFs and CDFs of multivariate normal distributions
458(1)
9.3.5 Outliers, quartiles and box plots
459(3)
9.4 Statistical Estimations
462(7)
9.4.1 Parametric estimation and interval estimation
462(1)
9.4.2 Multivariate linear regression and interval estimation
463(3)
9.4.3 Nonlinear least squares parametric and interval estimations
466(2)
9.4.4 Maximum likelihood estimations
468(1)
9.5 Statistical Hypothesis Tests
469(5)
9.5.1 Concept and procedures for statistic hypothesis test
469(2)
9.5.2 Hypothesis tests for distributions
471(3)
9.6 Analysis of Variance
474(4)
9.6.1 One-way ANOVA
474(2)
9.6.2 Two-way ANOVA
476(2)
9.6.3 n-way ANOVA
478(1)
9.7 Principal Component Analysis
478(2)
Exercises
480(3)
Bibliography
483(2)
10 Topics on Nontraditional Mathematical Branches 485(84)
10.1 Fuzzy Logic and Fuzzy Inference
485(11)
10.1.1 MATLAB solutions to classical set problems
485(3)
10.1.2 Fuzzy sets and membership functions
488(6)
10.1.3 Fuzzy rules and fuzzy inference
494(2)
10.2 Rough Set Theory and Its Applications
496(6)
10.2.1 Introduction to rough set theory
496(3)
10.2.2 Data processing problem solutions using rough sets
499(3)
10.3 Neural Network and Applications in Data Fitting Problems
502(14)
10.3.1 Fundamentals of neural networks
503(1)
10.3.2 Feedforward neural network
504(7)
10.3.3 Radial basis neural networks and applications
511(3)
10.3.4 Graphical user interface for neural networks
514(2)
10.4 Evolutionary Computing and Global Optimization Problem Solutions
516(13)
10.4.1 Basic idea of genetic algorithms
517(1)
10.4.2 Solutions to optimization problems with genetic algorithms
518(4)
10.4.3 Solving constrained problems
522(1)
10.4.4 Solving optimization problems with Global Optimization Toolbox
522(6)
10.4.5 Towards accurate global minimum solutions
528(1)
10.5 Wavelet Transform and Its Applications in Data Processing
529(9)
10.5.1 Wavelet transform and waveforms of wavelet bases
530(4)
10.5.2 Wavelet transform in signal processing problems
534(4)
10.5.3 Graphical user interface in wavelets
538(1)
10.6 Fractional-order Calculus
538(26)
10.6.1 Definitions of fractional-order calculus
539(1)
10.6.2 Properties and relationship of various fractional-order differentiation definitions
540(1)
10.6.3 Evaluating fractional-order differentiation
541(6)
10.6.4 Solving fractional-order differential equations
547(6)
10.6.5 Block diagram based solutions of nonlinear fractional-order ordinary differential equations
553(4)
10.6.6 Object-oriented modeling and analysis of linear fractional-order systems
557(7)
Exercises
564(3)
Bibliography
567(2)
MATLAB Functions Index 569(8)
Index 577
Dingyü Xue is a professor of control engineering in the College of Information Science and Engineering at Northeastern University in China. Dr. Xue is the author or coauthor of many books on MATLAB®-based control, simulation, and mathematical problem solutions, including Computer Aided Control Systems Design with MATLAB, Solving Advanced Applied Mathematical Problems Using MATLAB, and System Simulation Techniques with MATLAB and Simulink. His current research interests include CAD of control systems, system simulation, and fractional order control. He earned his D.Phil. from Sussex University.

YangQuan Chen is the director and founder of the Mechatronics, Embedded Systems and Automation (MESA) Lab in the School of Engineering at the University of California, Merced. He is the topic editor-in-chief of field robotics for the International Journal of Advanced Robotic Systems, a founding editorial board member of Unmanned Systems, and an editorial board member of several other leading journals. Dr. Chen is also the author or coauthor of many books, including Distributed-Order Dynamic Systems: Stability, Simulation, Applications and Perspectives, Fractional Order Motion Controls, Remote Sensing and Actuation Using Unmanned Vehicles, System Simulation Techniques with MATLAB and Simulink, and Modeling, Analysis and Design of Control Systems in MATLAB and Simulink. His research interests include unmanned aerial systems and UAV-based personal remote sensing, cyber-physical systems, the modeling and control of renewable energy systems, mechatronics, and applied fractional calculus. He earned his Ph.D. from Nanyang Technological University.
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