Numerical and analytical methods with MATLAB:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla [u.a.]
CRC Press
2009
|
| Series: | CRC series in computational mechanics and applied analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 452 S. Ill., graph. Darst. |
| ISBN: | 9781420093568 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical and analytical methods with MATLAB |c William Bober ; Chi-Tay Tsai ; Oren Masory |
| 264 | 1 | |a Boca Raton, Fla [u.a.] |b CRC Press |c 2009 | |
| 300 | |a XVIII, 452 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | Titel: Numerical and analytical methods with MATLAB
Autor: Bober, William
Jahr: 2009
Contents
Preface............................................................................................................xi
Acknowledgments.........................................................................................xv
Authors........................................................................................................xvii
1 Numerical Modeling for Engineering....................................................1
1.1 Computer Usage in Engineering........................................................1
1.1.1 Importance of the Computer................................................1
1.1.2 Computer Usage...................................................................1
1.2 The Mathematical Model..................................................................2
1.3 Computer Programming...................................................................2
1.4 Preparing a Computer Program.........................................................3
1.5 Recommended Procedures for Writing a Program.............................3
1.6 Building Blocks in Writing a Program...............................................3
2 MATLAB Fundamentals........................................................................5
2.1 Introduction......................................................................................5
2.1.1 The MATLAB Windows......................................................5
2.2 Constructing a Program in MATLAB...............................................8
2.3 The MATLAB Program....................................................................8
2.4 Program Examples...........................................................................18
2.5 Debugging a Program......................................................................26
2.6 3-D and Contour Plots....................................................................28
Projects......................................................................................................29
References.................................................................................................44
3 Matrices................................................................................................45
3.1 Matrix Operations...........................................................................45
3.2 System of Linear Equations.............................................................48
3.2.1 The inv Function................................................................49
3.2.2 The Gauss Elimination Function........................................49
3.2.3 Examples............................................................................50
v
vi ¦ Contents
3.3 Gauss Elimination...........................................................................55
3.4 The Gauss?Jordan Method..............................................................61
3.5 Number of Solutions.......................................................................63
3.6 Inverse Matrix................................................................................64
3.7 The Eigenvalue Problem..................................................................68
Exercises.....................................................................................................72
Projects......................................................................................................72
Reference...................................................................................................76
Roots of Algebraic and Transcendental Equations...............................77
4.1 The Search Method........................................................................77
4.2 Bisection Method...........................................................................77
4.3 Newton-Raphson Method..............................................................79
4.4 The fzero Function..........................................................................80
4.4.1 Example Programs.............................................................84
Projects......................................................................................................83
Reference...................................................................................................93
Numerical Integration..........................................................................95
5.1 Numerical Integration and Simpson s Rule......................................95
5.2 Improper Integrals...........................................................................98
5.3 MATLAB s Quad Function...........................................................100
5.4 MATLAB s DBLQUAD Function................................................101
Exercises...................................................................................................102
Projects....................................................................................................103
Numerical Integration of Ordinary Differential Equations...............105
6.1 The Initial Value Problem..............................................................105
6.2 The Fourth-Order Runge-Kutta Method......................................107
6.3 System of Two First-Order Equations............................................108
6.4 A Single Second-Order Equation...................................................108
6.5 MATLAB s ODE Function...........................................................110
6.6 Ordinary Differential Equations That Are Not
Initial Value Problems...................................................................112
6.7 Solution of a Tri-Diagonal System of Linear Equations.................112
6.8 Difference Formulas......................................................................115
6.9 Deflection of a Beam.....................................................................118
Projects....................................................................................................121
Simulink............................................................................................. 1
7.1 Introduction..................................................................................141
7.2 Creating a Model in Simulink.......................................................141
7.3 Typical Building Blocks in Constructing a Model.........................143
Contents ¦ vii
7.4 Constructing and Running the Model..........................................146
7.5 Constructing a Subsystem.............................................................146
7.6 Using the mux and fen Blocks.......................................................146
7.7 The Relay Block.............................................................................148
7.8 The Switch Block...........................................................................149
7.9 Trigonometric Function Blocks.....................................................150
Projects....................................................................................................152
8 Curve Fitting......................................................................................155
8.1 Curve-Fitting Objective.................................................................155
8.2 Method of Least Squares...............................................................155
8.3 Curve Fitting with the Exponential Function................................158
8.4 MATLAB s Curve-Fitting Function..............................................160
8.5 Cubic Splines.................................................................................162
8.6 The Function Interpl for Cubic Spline Curve Fitting....................164
8.7 Curve Fitting with Fourier Series..................................................164
Projects....................................................................................................167
9 Optimization......................................................................................171
9.1 Introduction..................................................................................171
9.2 Unconstrained Optimization Problems.........................................172
9.3 Method of Steepest Descent..........................................................173
9.4 Optimization with Constraints.....................................................176
9.5 MATLAB s Optimization Function..............................................178
Exercises...................................................................................................182
Projects....................................................................................................182
Reference.................................................................................................186
10 Partial Differential Equations............................................................187
10.1 The Classification of Partial Differential Equations.......................187
10.2 Solution by Separation of Variables................................................188
10.2.1 The Vibrating String.........................................................188
10.2.2 Unsteady Heat Transfer I (Bar).........................................192
10.2.3 Unsteady Heat Transfer II (Cylinder)...............................199
10.3 Unsteady Heat Transfer in 2-D....................................................206
10.4 Perturbation Theory and Sound Waves..........................................211
10.5 Review of Finite Difference Formulas............................................217
10.6 Example of Applying Finite Difference Methods to Partial
Differential Equations...................................................................217
10.6.1 The Explicit Method.........................................................218
10.6.2 The Implicit Method.......................................................220
Projects....................................................................................................221
viii ¦ Contents
11 Iteration Method................................................................................233
11.1 Iteration in Pipe Flow Analysis......................................................233
11.2 The Gauss-Seidel Method.............................................................235
11.3 The Hardy-Cross Method.............................................................238
Projects....................................................................................................241
References................................................................................................248
12 Laplace Transforms............................................................................249
12.1 Laplace Transform and Inverse Transform....................................249
12.2 Transforms of Derivatives..............................................................256
12.3 Ordinary Differential Equations, Initial Value Problem................257
12.4 A Shifting Theorem......................................................................260
12.5 The Unit Step Function.................................................................263
12.6 Laplace Transform of the Unit Step Function...............................264
12.7 Convolution.................................................................................268
12.8 Laplace Transforms Applied to Partial Differential Equations.......271
12.9 Laplace Transforms and Complex Variables..................................276
12.9.1 Residues and Poles............................................................278
Exercises...................................................................................................281
References................................................................................................282
13 An Introduction to the Finite Element Method.................................283
13.1 Finite Element Method for Stress Analysis....................................283
13.2 Structural Mechanics Plane Stress Analysis...................................283
13.3 The Shape Function for a Linear Triangle Element........................288
13.3.1 3-Node Triangular Element for 2-D Stress Analysis.........290
13.3.2 Shape Function in Area Coordinates................................291
13.3.3 Finite Element Formulation Using Triangular
Elements...........................................................................292
13.4 Finite Element Analysis Using MATLAB s PDE Toolbox.............299
13.5 Structural Mechanics Plane Strain Analysis..................................320
13.6 Model Analysis of 2-D Structures.................................................321
13.7 Finite Element Analysis for Heat Transfer.....................................325
Projects....................................................................................................339
References................................................................................................341
14 Control Systems.................................................................................343
14.1 Introduction.................................................................................343
14.2 Representation of Systems in MATLAB.......................................346
14.2.1 Transfer Function Representation....................................348
14.2.2 Zero-Pole-Gain Format of Transfer Function
Representation..................................................................350
14.2.3 State Space Representation...............................................352
Contents ¦ ix
14.3 Closed-Loop Systems.....................................................................355
14.3.1 DC Motor Modeling........................................................355
14.3.2 Block Diagrams................................................................357
14.3.3 MATLAB Tools for Defining the Closed-Loop System....358
14.4 MATLAB Tools for the Performance Analysis
of Closed-Loop Systems.................................................................361
14.4.1 Root Locus Plots...............................................................361
14.4.2 Nyquist Plots....................................................................363
14.5 MATLAB s SISOtool....................................................................367
14.5.1 Example to Be Used with SISOtool..................................367
14.5.2 SISOtool Main Features...................................................370
14.5.3 Using SISOtool to Design the Controller for Example
at Beginning of This Section.............................................371
14.6 Application of Simulink in Controls and Dynamic Systems..........377
14.6.1 Example of Control of the Fluid Level in Coupled
Tanks................................................................................377
14.6.2 Design of a Feed-Forward Loop Using Optimality
Criteria.............................................................................385
14.6.3 Active Suspension.............................................................391
14.6.4 Sampled Data Control System..........................................394
14.6.5 Implementation of ADC and DAC in Simulink...............397
14.7 Simulink s Data Acquisition Toolbox............................................405
14.7.1 Analog Input...................................................................406
14.7.2 Analog Output.................................................................407
14.7.3 Digital Input....................................................................408
14.7.4 Digital Output................................................................408
Projects....................................................................................................412
Endnotes..................................................................................................417
Appendix A..................................................................................................419
Appendix B..................................................................................................423
Appendix C.................................................................................................429
Index...........................................................................................................439
|
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| spelling | Bober, William Verfasser aut Numerical and analytical methods with MATLAB William Bober ; Chi-Tay Tsai ; Oren Masory Boca Raton, Fla [u.a.] CRC Press 2009 XVIII, 452 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRC series in computational mechanics and applied analysis Includes bibliographical references and index MATLAB Datenverarbeitung Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s MATLAB (DE-588)4329066-8 s DE-604 Tsai, Chi-Tay Verfasser aut Masory, Oren Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017751807&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bober, William Tsai, Chi-Tay Masory, Oren Numerical and analytical methods with MATLAB MATLAB Datenverarbeitung Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4329066-8 |
| title | Numerical and analytical methods with MATLAB |
| title_auth | Numerical and analytical methods with MATLAB |
| title_exact_search | Numerical and analytical methods with MATLAB |
| title_full | Numerical and analytical methods with MATLAB William Bober ; Chi-Tay Tsai ; Oren Masory |
| title_fullStr | Numerical and analytical methods with MATLAB William Bober ; Chi-Tay Tsai ; Oren Masory |
| title_full_unstemmed | Numerical and analytical methods with MATLAB William Bober ; Chi-Tay Tsai ; Oren Masory |
| title_short | Numerical and analytical methods with MATLAB |
| title_sort | numerical and analytical methods with matlab |
| topic | MATLAB Datenverarbeitung Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB Datenverarbeitung Numerical analysis Data processing Numerische Mathematik |
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