Solving applied mathematical problems with MATLAB:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 432 S. Ill., graph. Darst. |
| ISBN: | 9781420082500 1420082507 |
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MARC
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| 010 | |a 2008025953 | ||
| 020 | |a 9781420082500 |c (hbk.) |9 978-1-420-08250-0 | ||
| 020 | |a 1420082507 |9 1-420-08250-7 | ||
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| 082 | 0 | |a 510.285/5133 | |
| 084 | |a ST 601 |0 (DE-625)143682: |2 rvk | ||
| 100 | 1 | |a Xue, Dingyü |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Solving applied mathematical problems with MATLAB |c Dingyu Xue ; YangQuan Chen |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a XIV, 432 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 630 | 0 | 4 | |a MATLAB |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Engineering mathematics |x Data processing | |
| 650 | 4 | |a Numerical analysis |x Data processing | |
| 650 | 4 | |a Mathematical optimization |x Data processing | |
| 650 | 0 | 7 | |a Technische Mathematik |0 (DE-588)4827059-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a MATLAB |0 (DE-588)4329066-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Technische Mathematik |0 (DE-588)4827059-3 |D s |
| 689 | 0 | 1 | |a MATLAB |0 (DE-588)4329066-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Chen, Yangquan |d 1966- |e Verfasser |0 (DE-588)121213277 |4 aut | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0838/2008025953-d.html |3 Publisher description | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016960979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016960979 | |
Record in the Search Index
| _version_ | 1808044201960538112 |
|---|---|
| adam_text |
Contents
Preface
xi
1 Computer
Mathematics Languages
—
An Overview
1
1.1
Computer Solutions to Mathematics Problems
. 1
1.1.1
Why should we study computer mathematics language?
1
1.1.2
Analytical solutions versus numerical solutions
. 4
1.1.3
Mathematics software packages: an overview
. 5
1.2
Summary of Computer Mathematics Languages
. 6
1.2.1
A brief historic review of
MATLAB
. 6
1.2.2
Three widely used computer mathematics languages
. 7
1.2.3
Introduction to free scientific open-source softwares
. . 7
1.3
Outline of the Book
. 8
Exercises
. 9
2
Fundamentals of
MATLAB
Programming
11
2.1
Fundamentals of
MATLAB
Programming
. 12
2.1.1
Variables and constants in
MATLAB
. 12
2.1.2
Data structure
. 13
2.1.3
Basic structure of
MATLAB
. 14
2.1.4
Colon expressions and sub-matrices extraction
. 15
2.2
Fundamental Mathematical Calculations
. 16
2.2.1
Algebraic operations of matrices
. 16
2.2.2
Logic operations of matrices
. 18
2.2.3
Relationship operations of matrices
. 19
2.2.4
Simplifications and presentations of analytical results
. 19
2.2.5
Basic number theory computations
. 21
2.3
Flow Control Structures of
MATLAB
Language
. 22
2.3.1
Loop control structures
. 22
2.3.2
Conditional control structures
. 24
2.3.3
Switch structure
. 25
2.3.4
Trial structure
. 26
2.4
Writing and Debugging
MATLAB
Functions
. 27
2.4.1
Basic structure of
MATLAB
functions
. 27
2.4.2
Programming of functions with variable inputs/outputs
30
2.4.3
Inline functions and anonymous functions
. 31
2.5
Two-Dimensional Graphics
. 31
2.5.1
Basic statements of two-dimensional plotting
. 32
2.5.2
Other two-dimensional plotting statements
. 34
2.5.3
Implicit function plotting and applications
. 36
vi
Solving
Applied
Mathematical Problems with
MATLAB
2.5.4
Graphics decorations
. 36
2.6
Three-Dimensional Graphics
. 39
2.6.1
Plotting of three-dimensional curves
. 39
2.6.2
Plotting of three-dimensional surfaces
. 40
2.6.3
Viewpoint setting in
3D
graphs
. 43
Exercises
. 44
3
Calculus Problems
47
3.1
Analytical Solutions to Calculus Problems
. 47
3.1.1
Analytical solutions to limit problems
. 48
3.1.2
Analytical solutions to derivative problems
. 50
3.1.3
Analytical solutions to integral problems
. 55
3.2
Series Expansions and Series Evaluations
. 58
3.2.1
Taylor series expansion
. 59
3.2.2
Fourier series expansion
. 62
3.2.3
Series
. 65
3.2.4
Sequence product
. 67
3.3
Numerical Differentiation
. 67
3.3.1
Numerical differentiation algorithms
. 68
3.3.2
Central-point difference algorithm
. 69
3.3.3
Gradient computations of functions with two variables
71
3.4
Numerical Integration Problems
. 72
3.4.1
Numerical integration from given data using trapezoidal
method
. 72
3.4.2
Numerical integration of single variable functions
. 74
3.4.3
Numerical solutions to double integrals
. 77
3.4.4
Numerical solutions to triple integrals
. 79
3.5
Path Integrals and Line Integrals
. 80
3.5.1
Path integrals
. 80
3.5.2
Line integrals
. 81
3.6
Surface Integrals
. 83
3.6.1
Scalar surface integrals
. 83
3.6.2
Vector surface integrals
. 84
Exercises
. 85
4
Linear Algebra Problems
89
4.1
Inputting Special Matrices
. 90
4.1.1
Numerical matrix input
. 90
4.1.2
Defining symbolic matrices
. 94
4.2
Fundamental Matrix Operations
. 95
4.2.1
Basic concepts and properties of matrices
. 95
4.2.2
Matrix inversion and generalized inverse of a matrix
. 102
4.2.3
Matrix eigenvalue problems
. 106
4.3
Fundamental Matrix Transformations
. 109
4.3.1
Similarity transformations and orthogonal matrices
. . 109
4.3.2
Triangular and Cholesky decompositions
.
Ill
4.3.3
Jordan transformations
. 114
4.3.4
Singular value decompositions
. 116
Contents
vii
4.4
Solving Matrix Equations
. 118
4.4.1
Solutions to linear algebraic equations
. 118
4.4.2
Solutions to Lyapunov equations
. 121
4.4.3
Solutions to Sylvester equations
. 124
4.4.4
Solutions to Riccati equations
. 125
4.5
Nonlinear Functions and Matrix Function Evaluations
. 126
4.5.1
Element-by-element computations
. 126
4.5.2
Matrix function evaluations
. 127
Exercises
. 133
Integral Transforms and Complex Variable Functions
137
5.1
Laplace Transforms and Their Inverses
. 137
5.1.1
Definitions and properties
. 138
5.1.2
Computer solution to Laplace transform problems
. 139
5.2
Fourier Transforms and Their Inverses
. 142
5.2.1
Definitions and properties
. 142
5.2.2
Solving Fourier transform problems
. 142
5.2.3
Fourier sine and cosine transforms
. 144
5.2.4
Discrete Fourier sine, cosine transforms
. 147
5.3
Other Integral Transforms
. 147
5.3.1
Mellin transform
. 148
5.3.2
Hankel transform solutions
. 149
5.4
Z
Transforms and Their Inverses
. 150
5.4.1
Definitions and properties of
Z
transforms and inverses
150
5.4.2
Computations of
Z
transform
. 151
5.5
Solving Complex Variable Function Problems
. 152
5.5.1
Complex variable functions and mapping visualization
152
5.5.2
Concept and computation of residues
. 152
5.5.3
Partial fraction expansion for rational functions
. 155
5.5.4
Inverse Laplace transform using PFEs
. 159
5.5.5
Computing closed-path integrals
. 160
Exercises
. 162
Nonlinear Equations and Numerical Optimization Problems
165
6.1
Nonlinear Algebraic Equations
. 166
6.1.1
Graphical method for solving nonlinear equations
. . . 166
6.1.2
Quasi-analytical solutions to polynomial-type equations
168
6.1.3
Numerical solutions to general nonlinear equations
. . 172
6.1.4
Nonlinear matrix equations
. 174
6.2
Unconstrained Optimization Problems
. 176
6.2.1
Analytical solutions and graphical solution methods
. . 176
6.2.2
Numerical solution of unconstrained optimization using
MATLAB
. 178
6.2.3
Global minimum and local minima
. 179
6.2.4
Solving optimization problems with gradients
. 181
6.2.5
Optimization problems with bounded constraints
. 182
6.3
Constrained Optimization Problems
. 183
6.3.1
Constraints and feasibility regions
. 184
viii
Solving
Applied
Mathematical Problems with
MATLAB
6.3.2
Solving linear programming problems
. 185
6.3.3
Solving quadratic programming problems
. 187
6.3.4
Solving general nonlinear programming problems
. . . 188
6.4
Mixed Integer Programming Problems
. 191
6.4.1
Solving mixed integer programming problems
. 191
6.4.2
Solving binary programming problems
. 194
6.5
Linear Matrix Inequalities
. 195
6.5.1
A general introduction to LMIs
. 196
6.5.2
Lyapunov inequalities
. 196
6.5.3
Classification of LMI problems
. 198
6.5.4
LMI problem solutions with
MATLAB
. 199
6.5.5
Optimization of LMI problems by YALMIP Toolbox
. 201
Exercises
. 203
7
Differential Equation Problems
207
7.1
Analytical Solution Methods for Special Classes of ODEs
. . 208
7.1.1
Mathematical descriptions
. 208
7.1.2
Analytical solution methods
. 210
7.1.3
Applications of Laplace transforms
. 212
7.1.4
Analytical solutions to LTI state-space equations
. 214
7.1.5
Analytical solutions to special nonlinear differential
equations
. 215
7.2
Numerical Solutions to ODEs
. 215
7.2.1
Overview of numerical solution algorithms
. 216
7.2.2
Fixed-step Runge-Kutta algorithm and its
MATLAB
implementation
. 218
7.2.3
Numerical solution to first-order vector ODEs
. 219
7.2.4
Transforms to standard ODEs
. 224
7.2.5
Validation of numerical solutions to ODEs
. 231
7.3
Numerical Solutions to Special Ordinary Differential Equations
232
7.3.1
Solutions of stiff ODEs
. 232
7.3.2
Solutions of implicit differential equations
. 235
7.3.3
Solutions to differential algebraic equations
. 239
7.3.4
Solutions to delay differential equations
. 241
7.4
Solving Boundary Value Problems
. 243
7.4.1
Solutions to two-point boundary value problems
. 243
7.4.2
Solutions to general boundary value problems
. 245
7.5
Introduction to Partial Differential Equations
. 247
7.5.1
Solving a set of ID PDEs
. 248
7.5.2
Mathematical description to 2D PDEs
. 249
7.5.3
The GUI for the PDE Toolbox
—
an introduction
. 251
7.6
Solving ODEs with Block Diagrams in Simulink
. 258
7.6.1
A brief introduction to Simulink
. 258
7.6.2
Simulink
—
relevant blocks
. 258
7.6.3
Using Simulink for modeling
ала
simulation of ODEs
. 260
Exercises
. 263
Contents ix
Data Interpolation
and Functional
Approximation Problems 269
8.1 Interpolation
and Data Fitting
. 270
8.1.1
One-dimensional data interpolation
. 270
8.1.2
Definite integral evaluation from given samples
. 273
8.1.3
Two-dimensional grid data interpolation
. 275
8.1.4
Two-dimensional scattered data interpolation
. 277
8.1.5
High-dimensional data interpolations
. 280
8.2
Spline Interpolation and Numerical Calculus
. 281
8.2.1
Spline interpolation in
MATLAB
. 281
8.2.2
Numerical differentiation and integration with splines
284
8.3
Data Modeling
. 287
8.3.1
Polynomial fitting
. 287
8.3.2
Approximation by continued fraction expansions
. 290
8.3.3
Padé
rational approximations
. 292
8.3.4
Curve fitting by linear combination of basis functions
. 294
8.3.5
Least squares curve fitting
. 296
8.4
Signal Analysis and Digital Signal Processing
. 298
8.4.1
Correlation analysis
. 298
8.4.2
Fast Fourier transforms
. 300
8.4.3
Filtering techniques and filter design
. 302
Exercises
. 306
Probability and Mathematical Statistics Problems
309
9.1
Distributions and
Pseudo-
Random Number Generators
. . . 309
9.1.1
Introduction to PDFs and CDFs
. 309
9.1.2
PDFs/CDFs of commonly used distributions
. 310
9.1.3
Solving probability problems
. 317
9.1.4
Random numbers and pseudo-random numbers
. 318
9.2
Statistics
. 319
9.2.1
Mean and variance of random variables
. 319
9.2.2
Moments of random variables
. 321
9.2.3
Covariance analysis of multivariate random variables
. 322
9.2.4
Multivariate normal distributions
. 323
9.2.5
Monte Carlo solutions to mathematical problems
. . . 324
9.3
Statistical Analysis
. 326
9.3.1
Parametric estimation and interval estimation
. 326
9.3.2 Multivariable
linear regression and interval estimation
328
9.3.3
Nonlinear parametric and interval estimations
. 330
9.4
Statistic Hypothesis Tests
. 333
9.4.1
Basic concept and procedures for statistic hypothesis
test
. 333
9.4.2
Solving hypothesis test problems in
MATLAB
. 334
9.5
Analysis of Variance and Its Computation
. 337
9.5.1
One-way ANOVA
. 337
9.5.2
Two-way ANOVA
. 339
9.5.3
η
-way ANOVA
. 341
Exercises
. 341
χ
Solving Applied Mathematical Problems with
MATLAB
10
Nontraditional
Solution Methods
345
10.1
Fuzzy Logic and Fuzzy Inference
. 346
10.1.1
Classical set theory and fuzzy sets
. 346
10.1.2
Membership function and fuzzification
. 349
10.1.3
An interactive membership function editor
. 351
10.1.4
Building fuzzy inference systems
. 351
10.1.5
Fuzzy rules and fuzzy inference
. 353
10.2
Neural Network and Its Applications in Data Fitting Problems
356
10.2.1
Fundamentals of neural networks
. 357
10.2.2
Graphical user interface for neural networks
. 364
10.3
Evolution Algorithms and Their Applications in Optimization
Problems
. 366
10.3.1
Basic idea of genetic algorithms
. 366
10.3.2
MATLAB
solutions to optimization problems with
genetic algorithms
. 368
10.3.3
Particle swarm optimizations
. 373
10.3.4
Solving optimization problems with GADS Toolbox
. . 374
10.3.5
Towards accurate global minimum solutions
. 377
10.4
Wavelet Transform and Its Applications in Data Processing
. 378
10.4.1
Wavelet transform and waveforms of wavelet bases
. . 378
10.4.2
Wavelet transform in signal processing problems
. 383
10.4.3
Graphical user interface in wavelets
. 386
10.5
Rough Set Theory and Its Applications
. 388
10.5.1
Introduction to rough set theory
. 388
10.5.2
Data processing problem solutions using rough sets
. . 391
10.6
Fractional-Order Calculus
. 395
10.6.1
Definitions of fractional-order calculus
. 395
10.6.2
Evaluating fractional-order differentiation
. 400
10.6.3
Solving fractional-order differential equations
. 405
Exercises
. 412
References and Bibliography
415
MATLAB
Functions Index
419
Index
425 |
| adam_txt |
Contents
Preface
xi
1 Computer
Mathematics Languages
—
An Overview
1
1.1
Computer Solutions to Mathematics Problems
. 1
1.1.1
Why should we study computer mathematics language?
1
1.1.2
Analytical solutions versus numerical solutions
. 4
1.1.3
Mathematics software packages: an overview
. 5
1.2
Summary of Computer Mathematics Languages
. 6
1.2.1
A brief historic review of
MATLAB
. 6
1.2.2
Three widely used computer mathematics languages
. 7
1.2.3
Introduction to free scientific open-source softwares
. . 7
1.3
Outline of the Book
. 8
Exercises
. 9
2
Fundamentals of
MATLAB
Programming
11
2.1
Fundamentals of
MATLAB
Programming
. 12
2.1.1
Variables and constants in
MATLAB
. 12
2.1.2
Data structure
. 13
2.1.3
Basic structure of
MATLAB
. 14
2.1.4
Colon expressions and sub-matrices extraction
. 15
2.2
Fundamental Mathematical Calculations
. 16
2.2.1
Algebraic operations of matrices
. 16
2.2.2
Logic operations of matrices
. 18
2.2.3
Relationship operations of matrices
. 19
2.2.4
Simplifications and presentations of analytical results
. 19
2.2.5
Basic number theory computations
. 21
2.3
Flow Control Structures of
MATLAB
Language
. 22
2.3.1
Loop control structures
. 22
2.3.2
Conditional control structures
. 24
2.3.3
Switch structure
. 25
2.3.4
Trial structure
. 26
2.4
Writing and Debugging
MATLAB
Functions
. 27
2.4.1
Basic structure of
MATLAB
functions
. 27
2.4.2
Programming of functions with variable inputs/outputs
30
2.4.3
Inline functions and anonymous functions
. 31
2.5
Two-Dimensional Graphics
. 31
2.5.1
Basic statements of two-dimensional plotting
. 32
2.5.2
Other two-dimensional plotting statements
. 34
2.5.3
Implicit function plotting and applications
. 36
vi
Solving
Applied
Mathematical Problems with
MATLAB
2.5.4
Graphics decorations
. 36
2.6
Three-Dimensional Graphics
. 39
2.6.1
Plotting of three-dimensional curves
. 39
2.6.2
Plotting of three-dimensional surfaces
. 40
2.6.3
Viewpoint setting in
3D
graphs
. 43
Exercises
. 44
3
Calculus Problems
47
3.1
Analytical Solutions to Calculus Problems
. 47
3.1.1
Analytical solutions to limit problems
. 48
3.1.2
Analytical solutions to derivative problems
. 50
3.1.3
Analytical solutions to integral problems
. 55
3.2
Series Expansions and Series Evaluations
. 58
3.2.1
Taylor series expansion
. 59
3.2.2
Fourier series expansion
. 62
3.2.3
Series
. 65
3.2.4
Sequence product
. 67
3.3
Numerical Differentiation
. 67
3.3.1
Numerical differentiation algorithms
. 68
3.3.2
Central-point difference algorithm
. 69
3.3.3
Gradient computations of functions with two variables
71
3.4
Numerical Integration Problems
. 72
3.4.1
Numerical integration from given data using trapezoidal
method
. 72
3.4.2
Numerical integration of single variable functions
. 74
3.4.3
Numerical solutions to double integrals
. 77
3.4.4
Numerical solutions to triple integrals
. 79
3.5
Path Integrals and Line Integrals
. 80
3.5.1
Path integrals
. 80
3.5.2
Line integrals
. 81
3.6
Surface Integrals
. 83
3.6.1
Scalar surface integrals
. 83
3.6.2
Vector surface integrals
. 84
Exercises
. 85
4
Linear Algebra Problems
89
4.1
Inputting Special Matrices
. 90
4.1.1
Numerical matrix input
. 90
4.1.2
Defining symbolic matrices
. 94
4.2
Fundamental Matrix Operations
. 95
4.2.1
Basic concepts and properties of matrices
. 95
4.2.2
Matrix inversion and generalized inverse of a matrix
. 102
4.2.3
Matrix eigenvalue problems
. 106
4.3
Fundamental Matrix Transformations
. 109
4.3.1
Similarity transformations and orthogonal matrices
. . 109
4.3.2
Triangular and Cholesky decompositions
.
Ill
4.3.3
Jordan transformations
. 114
4.3.4
Singular value decompositions
. 116
Contents
vii
4.4
Solving Matrix Equations
. 118
4.4.1
Solutions to linear algebraic equations
. 118
4.4.2
Solutions to Lyapunov equations
. 121
4.4.3
Solutions to Sylvester equations
. 124
4.4.4
Solutions to Riccati equations
. 125
4.5
Nonlinear Functions and Matrix Function Evaluations
. 126
4.5.1
Element-by-element computations
. 126
4.5.2
Matrix function evaluations
. 127
Exercises
. 133
Integral Transforms and Complex Variable Functions
137
5.1
Laplace Transforms and Their Inverses
. 137
5.1.1
Definitions and properties
. 138
5.1.2
Computer solution to Laplace transform problems
. 139
5.2
Fourier Transforms and Their Inverses
. 142
5.2.1
Definitions and properties
. 142
5.2.2
Solving Fourier transform problems
. 142
5.2.3
Fourier sine and cosine transforms
. 144
5.2.4
Discrete Fourier sine, cosine transforms
. 147
5.3
Other Integral Transforms
. 147
5.3.1
Mellin transform
. 148
5.3.2
Hankel transform solutions
. 149
5.4
Z
Transforms and Their Inverses
. 150
5.4.1
Definitions and properties of
Z
transforms and inverses
150
5.4.2
Computations of
Z
transform
. 151
5.5
Solving Complex Variable Function Problems
. 152
5.5.1
Complex variable functions and mapping visualization
152
5.5.2
Concept and computation of residues
. 152
5.5.3
Partial fraction expansion for rational functions
. 155
5.5.4
Inverse Laplace transform using PFEs
. 159
5.5.5
Computing closed-path integrals
. 160
Exercises
. 162
Nonlinear Equations and Numerical Optimization Problems
165
6.1
Nonlinear Algebraic Equations
. 166
6.1.1
Graphical method for solving nonlinear equations
. . . 166
6.1.2
Quasi-analytical solutions to polynomial-type equations
168
6.1.3
Numerical solutions to general nonlinear equations
. . 172
6.1.4
Nonlinear matrix equations
. 174
6.2
Unconstrained Optimization Problems
. 176
6.2.1
Analytical solutions and graphical solution methods
. . 176
6.2.2
Numerical solution of unconstrained optimization using
MATLAB
. 178
6.2.3
Global minimum and local minima
. 179
6.2.4
Solving optimization problems with gradients
. 181
6.2.5
Optimization problems with bounded constraints
. 182
6.3
Constrained Optimization Problems
. 183
6.3.1
Constraints and feasibility regions
. 184
viii
Solving
Applied
Mathematical Problems with
MATLAB
6.3.2
Solving linear programming problems
. 185
6.3.3
Solving quadratic programming problems
. 187
6.3.4
Solving general nonlinear programming problems
. . . 188
6.4
Mixed Integer Programming Problems
. 191
6.4.1
Solving mixed integer programming problems
. 191
6.4.2
Solving binary programming problems
. 194
6.5
Linear Matrix Inequalities
. 195
6.5.1
A general introduction to LMIs
. 196
6.5.2
Lyapunov inequalities
. 196
6.5.3
Classification of LMI problems
. 198
6.5.4
LMI problem solutions with
MATLAB
. 199
6.5.5
Optimization of LMI problems by YALMIP Toolbox
. 201
Exercises
. 203
7
Differential Equation Problems
207
7.1
Analytical Solution Methods for Special Classes of ODEs
. . 208
7.1.1
Mathematical descriptions
. 208
7.1.2
Analytical solution methods
. 210
7.1.3
Applications of Laplace transforms
. 212
7.1.4
Analytical solutions to LTI state-space equations
. 214
7.1.5
Analytical solutions to special nonlinear differential
equations
. 215
7.2
Numerical Solutions to ODEs
. 215
7.2.1
Overview of numerical solution algorithms
. 216
7.2.2
Fixed-step Runge-Kutta algorithm and its
MATLAB
implementation
. 218
7.2.3
Numerical solution to first-order vector ODEs
. 219
7.2.4
Transforms to standard ODEs
. 224
7.2.5
Validation of numerical solutions to ODEs
. 231
7.3
Numerical Solutions to Special Ordinary Differential Equations
232
7.3.1
Solutions of stiff ODEs
. 232
7.3.2
Solutions of implicit differential equations
. 235
7.3.3
Solutions to differential algebraic equations
. 239
7.3.4
Solutions to delay differential equations
. 241
7.4
Solving Boundary Value Problems
. 243
7.4.1
Solutions to two-point boundary value problems
. 243
7.4.2
Solutions to general boundary value problems
. 245
7.5
Introduction to Partial Differential Equations
. 247
7.5.1
Solving a set of ID PDEs
. 248
7.5.2
Mathematical description to 2D PDEs
. 249
7.5.3
The GUI for the PDE Toolbox
—
an introduction
. 251
7.6
Solving ODEs with Block Diagrams in Simulink
. 258
7.6.1
A brief introduction to Simulink
. 258
7.6.2
Simulink
—
relevant blocks
. 258
7.6.3
Using Simulink for modeling
ала
simulation of ODEs
. 260
Exercises
. 263
Contents ix
Data Interpolation
and Functional
Approximation Problems 269
8.1 Interpolation
and Data Fitting
. 270
8.1.1
One-dimensional data interpolation
. 270
8.1.2
Definite integral evaluation from given samples
. 273
8.1.3
Two-dimensional grid data interpolation
. 275
8.1.4
Two-dimensional scattered data interpolation
. 277
8.1.5
High-dimensional data interpolations
. 280
8.2
Spline Interpolation and Numerical Calculus
. 281
8.2.1
Spline interpolation in
MATLAB
. 281
8.2.2
Numerical differentiation and integration with splines
284
8.3
Data Modeling
. 287
8.3.1
Polynomial fitting
. 287
8.3.2
Approximation by continued fraction expansions
. 290
8.3.3
Padé
rational approximations
. 292
8.3.4
Curve fitting by linear combination of basis functions
. 294
8.3.5
Least squares curve fitting
. 296
8.4
Signal Analysis and Digital Signal Processing
. 298
8.4.1
Correlation analysis
. 298
8.4.2
Fast Fourier transforms
. 300
8.4.3
Filtering techniques and filter design
. 302
Exercises
. 306
Probability and Mathematical Statistics Problems
309
9.1
Distributions and
Pseudo-
Random Number Generators
. . . 309
9.1.1
Introduction to PDFs and CDFs
. 309
9.1.2
PDFs/CDFs of commonly used distributions
. 310
9.1.3
Solving probability problems
. 317
9.1.4
Random numbers and pseudo-random numbers
. 318
9.2
Statistics
. 319
9.2.1
Mean and variance of random variables
. 319
9.2.2
Moments of random variables
. 321
9.2.3
Covariance analysis of multivariate random variables
. 322
9.2.4
Multivariate normal distributions
. 323
9.2.5
Monte Carlo solutions to mathematical problems
. . . 324
9.3
Statistical Analysis
. 326
9.3.1
Parametric estimation and interval estimation
. 326
9.3.2 Multivariable
linear regression and interval estimation
328
9.3.3
Nonlinear parametric and interval estimations
. 330
9.4
Statistic Hypothesis Tests
. 333
9.4.1
Basic concept and procedures for statistic hypothesis
test
. 333
9.4.2
Solving hypothesis test problems in
MATLAB
. 334
9.5
Analysis of Variance and Its Computation
. 337
9.5.1
One-way ANOVA
. 337
9.5.2
Two-way ANOVA
. 339
9.5.3
η
-way ANOVA
. 341
Exercises
. 341
χ
Solving Applied Mathematical Problems with
MATLAB
10
Nontraditional
Solution Methods
345
10.1
Fuzzy Logic and Fuzzy Inference
. 346
10.1.1
Classical set theory and fuzzy sets
. 346
10.1.2
Membership function and fuzzification
. 349
10.1.3
An interactive membership function editor
. 351
10.1.4
Building fuzzy inference systems
. 351
10.1.5
Fuzzy rules and fuzzy inference
. 353
10.2
Neural Network and Its Applications in Data Fitting Problems
356
10.2.1
Fundamentals of neural networks
. 357
10.2.2
Graphical user interface for neural networks
. 364
10.3
Evolution Algorithms and Their Applications in Optimization
Problems
. 366
10.3.1
Basic idea of genetic algorithms
. 366
10.3.2
MATLAB
solutions to optimization problems with
genetic algorithms
. 368
10.3.3
Particle swarm optimizations
. 373
10.3.4
Solving optimization problems with GADS Toolbox
. . 374
10.3.5
Towards accurate global minimum solutions
. 377
10.4
Wavelet Transform and Its Applications in Data Processing
. 378
10.4.1
Wavelet transform and waveforms of wavelet bases
. . 378
10.4.2
Wavelet transform in signal processing problems
. 383
10.4.3
Graphical user interface in wavelets
. 386
10.5
Rough Set Theory and Its Applications
. 388
10.5.1
Introduction to rough set theory
. 388
10.5.2
Data processing problem solutions using rough sets
. . 391
10.6
Fractional-Order Calculus
. 395
10.6.1
Definitions of fractional-order calculus
. 395
10.6.2
Evaluating fractional-order differentiation
. 400
10.6.3
Solving fractional-order differential equations
. 405
Exercises
. 412
References and Bibliography
415
MATLAB
Functions Index
419
Index
425 |
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| dewey-sort | 3510.285 45133 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
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| id | DE-604.BV035153768 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:47:46Z |
| indexdate | 2024-08-22T00:08:38Z |
| institution | BVB |
| isbn | 9781420082500 1420082507 |
| language | English |
| lccn | 2008025953 |
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| spelling | Xue, Dingyü Verfasser aut Solving applied mathematical problems with MATLAB Dingyu Xue ; YangQuan Chen Boca Raton [u.a.] CRC Press 2009 XIV, 432 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index MATLAB Datenverarbeitung Engineering mathematics Data processing Numerical analysis Data processing Mathematical optimization Data processing Technische Mathematik (DE-588)4827059-3 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 s MATLAB (DE-588)4329066-8 s DE-604 Chen, Yangquan 1966- Verfasser (DE-588)121213277 aut http://www.loc.gov/catdir/enhancements/fy0838/2008025953-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016960979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xue, Dingyü Chen, Yangquan 1966- Solving applied mathematical problems with MATLAB MATLAB Datenverarbeitung Engineering mathematics Data processing Numerical analysis Data processing Mathematical optimization Data processing Technische Mathematik (DE-588)4827059-3 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4827059-3 (DE-588)4329066-8 |
| title | Solving applied mathematical problems with MATLAB |
| title_auth | Solving applied mathematical problems with MATLAB |
| title_exact_search | Solving applied mathematical problems with MATLAB |
| title_exact_search_txtP | Solving applied mathematical problems with MATLAB |
| title_full | Solving applied mathematical problems with MATLAB Dingyu Xue ; YangQuan Chen |
| title_fullStr | Solving applied mathematical problems with MATLAB Dingyu Xue ; YangQuan Chen |
| title_full_unstemmed | Solving applied mathematical problems with MATLAB Dingyu Xue ; YangQuan Chen |
| title_short | Solving applied mathematical problems with MATLAB |
| title_sort | solving applied mathematical problems with matlab |
| topic | MATLAB Datenverarbeitung Engineering mathematics Data processing Numerical analysis Data processing Mathematical optimization Data processing Technische Mathematik (DE-588)4827059-3 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB Datenverarbeitung Engineering mathematics Data processing Numerical analysis Data processing Mathematical optimization Data processing Technische Mathematik |
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