Solving applied mathematical problems with MATLAB:
Gespeichert in:
Beteiligte Personen: | , |
---|---|
Format: | Buch |
Sprache: | Englisch |
Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2009
|
Schlagwörter: | |
Links: | http://www.loc.gov/catdir/enhancements/fy0838/2008025953-d.html 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 |
Beschreibung: | Includes bibliographical references and index |
Umfang: | XIV, 432 S. Ill., graph. Darst. |
ISBN: | 9781420082500 1420082507 |
Internformat
MARC
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020 | |a 9781420082500 |c (hbk.) |9 978-1-420-08250-0 | ||
020 | |a 1420082507 |9 1-420-08250-7 | ||
035 | |a (OCoLC)232257583 | ||
035 | |a (DE-599)BVBBV035153768 | ||
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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 MATLAB |0 (DE-588)4329066-8 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Technische Mathematik |0 (DE-588)4827059-3 |2 gnd |9 rswk-swf |
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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 |
Datensatz im Suchindex
_version_ | 1819352055404298240 |
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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
|
any_adam_object | 1 |
author | Xue, Dingyü Chen, Yangquan 1966- |
author_GND | (DE-588)121213277 |
author_facet | Xue, Dingyü Chen, Yangquan 1966- |
author_role | aut aut |
author_sort | Xue, Dingyü |
author_variant | d x dx y c yc |
building | Verbundindex |
bvnumber | BV035153768 |
callnumber-first | T - Technology |
callnumber-label | TA331 |
callnumber-raw | TA331 |
callnumber-search | TA331 |
callnumber-sort | TA 3331 |
callnumber-subject | TA - General and Civil Engineering |
classification_rvk | ST 601 |
ctrlnum | (OCoLC)232257583 (DE-599)BVBBV035153768 |
dewey-full | 510.285/5133 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 510 - Mathematics |
dewey-raw | 510.285/5133 |
dewey-search | 510.285/5133 |
dewey-sort | 3510.285 45133 |
dewey-tens | 510 - Mathematics |
discipline | Informatik Mathematik |
format | Book |
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id | DE-604.BV035153768 |
illustrated | Illustrated |
indexdate | 2024-12-20T13:24:20Z |
institution | BVB |
isbn | 9781420082500 1420082507 |
language | English |
lccn | 2008025953 |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016960979 |
oclc_num | 232257583 |
open_access_boolean | |
owner | DE-11 |
owner_facet | DE-11 |
physical | XIV, 432 S. Ill., graph. Darst. |
publishDate | 2009 |
publishDateSearch | 2009 |
publishDateSort | 2009 |
publisher | CRC Press |
record_format | marc |
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 MATLAB (DE-588)4329066-8 gnd Technische Mathematik (DE-588)4827059-3 gnd |
subject_GND | (DE-588)4329066-8 (DE-588)4827059-3 |
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_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 MATLAB (DE-588)4329066-8 gnd Technische Mathematik (DE-588)4827059-3 gnd |
topic_facet | MATLAB Datenverarbeitung Engineering mathematics Data processing Numerical analysis Data processing Mathematical optimization Data processing Technische Mathematik |
url | http://www.loc.gov/catdir/enhancements/fy0838/2008025953-d.html 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 |
work_keys_str_mv | AT xuedingyu solvingappliedmathematicalproblemswithmatlab AT chenyangquan solvingappliedmathematicalproblemswithmatlab |