A first course in differential equations, modeling, and simulation:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 331 S. graph. Darst. |
| ISBN: | 9781439850879 1439850879 |
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MARC
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Record in the Search Index
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| adam_text | Titel: A first course in differential equations, modeling, and simulation
Autor: Smith, Carlos A
Jahr: 2011
Contents
Preface......................................................................................................................xi
Authors.................................................................................................................xiii
1 Introduction.....................................................................................................1
1.1 An Introductory Example....................................................................1
1.2 Modeling................................................................................................4
1.3 Differential Equations..........................................................................5
1.4 Forcing Functions.................................................................................9
1.5 Book Objectives...................................................................................11
1.6 Summary..............................................................................................12
1.7 Problems...............................................................................................13
2 Objects in a Gravitational Field.................................................................15
2.1 An Example..........................................................................................15
2.2 Antidifferentiation: Technique for Solving First-Order
Ordinary Differential Equations......................................................17
2.3 Back to Section 2.1...............................................................................18
2.4 Another Example................................................................................19
2.5 Separation of Variables: Technique for Solving First-Order
Ordinary Differential Equations......................................................21
2.6 Back to Section 2.4...............................................................................21
2.7 Equations, Unknowns, and Degrees of Freedom...........................22
2.8 Summary..............................................................................................26
2.9 Problems...............................................................................................26
3 Classical Solutions of Ordinary Linear Differential Equations........29
3.1 Examples of Differential Equations................. ...............................29
3.1.1 Mechanical Translational: Chapter 5..................................29
3.1.2 Fluid System: Chapter 7........................................................30
3.1.3 Thermal System: Chapter 8..................................................31
3.1.4 Electrical Circuit: Chapter 9.................................................31
3.2 Definition of a Linear Differential Equation...................................32
3.3 Integrating Factor Method.................................................................34
3.3.1 Development of the Integrating Factor Method................36
3.4 Characteristic Equation......................................................................37
3.4.1 Qualitative Characteristic of System Response.................38
3.5 Undetermined Coefficients................................................................43
3.5.1 Multiple Forcing Functions..................................................56
3.6 Response of First- and Second-Order Systems...............................56
3.6.1 First-Order Systems...............................................................57
vii
viii Contents
3.6.1.1 Step Function Input................................................60
3.6.1.2 Sinusoidal Function Input.....................................63
3.6.2 Second-Order Systems..........................................................64
3.6.2.1 Step Function Input................................................67
3.6.2.2 Sinusoidal Function Input.....................................68
3.6.3 Underdamped Response......................................................69
3.6.3.1 Period of Oscillation..............................................69
3.6.3.2 Decay Ratio.............................................................70
3.6.3.3 Rise Time.................................................................70
3.6.3.4 Settling Time...........................................................71
3.6.3.5 Overshoot................................................................71
3.7 Application of the Mathematics to Design......................................72
3.8 Summary..............................................................................................74
3.9 Problems...............................................................................................75
4 Laplace Transforms......................................................................................81
4.1 Definition of the Laplace Transform................................................82
4.2 Properties and Theorems of the Laplace Transform.....................85
4.2.1 Linearity Property.................................................................86
4.2.2 Real Differentiation Theorem..............................................86
4.2.3 Real Integration Theorem.....................................................87
4.2.4 Real Translation Theorem.....................................................88
4.2.5 Final Value Theorem.............................................................89
4.2.6 Complex Differentiation Theorem......................................89
4.2.7 Complex Translation Theorem............................................89
4.2.8 Initial Value Theorem............................................................89
4.3 Solution of Differential Equations Using Laplace Transform......91
4.3.1 Inversion by Partial Fractions Expansion...........................93
4.3.1.1 Repeated Roots.......................................................96
4.3.1.2 Complex Roots........................................................97
4.3.2 Handlung Time Delays........................................................111
4.4 Transfer Functions............................................................................114
4.5 Algebraic Manipulations Using Laplace Transforms..................116
4.6 Deviation Variables...........................................................................120
4.7 First- and Second-Order Systems...................................................126
4.8 Summary............................................................................................127
4.9 Problems.............................................................................................127
5 Mechanical Systems: Translational........................................................137
5.1 Mechanical Law and Experimental Facts..................................... 137
5.1.1 Gravity Force........................................................................138
5.1.2 Springs...................................................................................138
5.1.3 Damping Forces...................................................................140
5.1.4 Dashpots (Pistons or Dampers).........................................142
5.1.5 Ideal Pulley...........................................................................142
Contents ix
5.2 Types of Systems...............................................................................143
5.2.1 Undamped System...............................................................143
5.2.2 Damped System...................................................................145
5.3 DAlembert s Principle and Free Body Diagrams........................146
5.4 Additional Examples........................................................................150
5.5 Vertical Systems.................................................................................159
5.6 Summary............................................................................................163
5.7 Problems.............................................................................................163
6 Mechanical Systems: Rotational.............................................................175
6.1 Mechanical Law, Moment of Inertia, and Torque.........................175
6.1.1 Mass Moment of Inertia......................................................177
6.1.2 Torque....................................................................................178
6.2 Torsion Springs..................................................................................182
6.3 Rotational Dampening.....................................................................184
6.4 Gears...................................................................................................188
6.5 Systems with Rotational and Translational Elements.................191
6.6 Summary............................................................................................193
6.7 Problems.............................................................................................194
7 Mass Balances.............................................................................................201
7.1 Conservation of Mass.......................................................................201
7.2 Flow Rates and Concentrations......................................................204
7.3 Flow Element and Experimental Facts..........................................205
7.4 Examples of Mass Balances.............................................................209
7.5 Summary............................................................................................215
7.6 Problems.............................................................................................215
8 Thermal Systems........................................................................................223
8.1 Conservation of Energy...................................................................223
8.2 Modes of Heat Transfer....................................................................224
8.3 Conduction.........................................................................................225
8.4 Convection.........................................................................................227
8.5 Conduction and Convection in Series............................................228
8.6 Accumulated or Stored Energy.......................................................230
8.7 Some Examples..................................................................................231
8.8 Heat Transfer in a Flow System......................................................240
8.9 Summary............................................................................................244
8.10 Problems.............................................................................................245
9 Electrical Systems.......................................................................................249
9.1 Some Definitions and Conventions................................................249
9.2 Electrical Laws and Electrical Components..................................250
9.2.1 Initial Conditions in Electrical Systems............................256
9.3 Examples of Electrical Circuits.......................................................257
Contents
9.4 Additional Examples........................................................................267
9.5 RC Circuits as Filters........................................................................278
9.5.1 High-Pass Filter....................................................................278
9.5.2 Low-Pass Filter.....................................................................281
9.6 Summary............................................................................................285
9.7 Problems.............................................................................................285
10 Numerical Simulation...............................................................................295
10.1 Numerical Solution of Differential Equations..............................295
10.2 Euler s Method for First-Order Ordinary Differential
Equations............................................................................................296
10.3 Euler s Method for Second-Order Ordinary Differential
Equations............................................................................................298
10.4 StepSize..............................................................................................300
10.5 More Sophisticated Methods...........................................................301
10.6 Representation of Differential Equations by Block Diagrams ... 301
10.6.1 Basic Blocks...........................................................................301
10.6.2 Guidelines for Constructing Block Diagrams.................304
10.6.3 Some Additional Examples................................................306
10.6.4 Some Additional Source Blocks.........................................309
10.6.4.1 Step Block.............¦.................................................310
10.6.4.2 Sine Wave..............................................................310
10.7 Additional Examples........................................................................311
10.8 Summary............................................................................................319
10.9 Problems.............................................................................................320
Index.....................................................................................................................327
|
| any_adam_object | 1 |
| author | Smith, Carlos A. Campbell, Scott W. |
| author_facet | Smith, Carlos A. Campbell, Scott W. |
| author_role | aut aut |
| author_sort | Smith, Carlos A. |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| spelling | Smith, Carlos A. Verfasser aut A first course in differential equations, modeling, and simulation Carlos A. Smith ; Scott W. Campbell Boca Raton [u.a.] CRC Press 2011 XIII, 331 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations Experimental design MATHEMATICS / Advanced bisacsh MATHEMATICS / Applied bisacsh TECHNOLOGY & ENGINEERING / Engineering (General) bisacsh Simulation (DE-588)4055072-2 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Differentialgleichung (DE-588)4012249-9 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Simulation (DE-588)4055072-2 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Mathematische Physik (DE-588)4037952-8 s Technische Mathematik (DE-588)4827059-3 s 2\p DE-604 Campbell, Scott W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022641705&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Smith, Carlos A. Campbell, Scott W. A first course in differential equations, modeling, and simulation Differential equations Experimental design MATHEMATICS / Advanced bisacsh MATHEMATICS / Applied bisacsh TECHNOLOGY & ENGINEERING / Engineering (General) bisacsh Simulation (DE-588)4055072-2 gnd Technische Mathematik (DE-588)4827059-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mathematische Physik (DE-588)4037952-8 gnd Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
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| title | A first course in differential equations, modeling, and simulation |
| title_auth | A first course in differential equations, modeling, and simulation |
| title_exact_search | A first course in differential equations, modeling, and simulation |
| title_full | A first course in differential equations, modeling, and simulation Carlos A. Smith ; Scott W. Campbell |
| title_fullStr | A first course in differential equations, modeling, and simulation Carlos A. Smith ; Scott W. Campbell |
| title_full_unstemmed | A first course in differential equations, modeling, and simulation Carlos A. Smith ; Scott W. Campbell |
| title_short | A first course in differential equations, modeling, and simulation |
| title_sort | a first course in differential equations modeling and simulation |
| topic | Differential equations Experimental design MATHEMATICS / Advanced bisacsh MATHEMATICS / Applied bisacsh TECHNOLOGY & ENGINEERING / Engineering (General) bisacsh Simulation (DE-588)4055072-2 gnd Technische Mathematik (DE-588)4827059-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mathematische Physik (DE-588)4037952-8 gnd Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Experimental design MATHEMATICS / Advanced MATHEMATICS / Applied TECHNOLOGY & ENGINEERING / Engineering (General) Simulation Technische Mathematik Mathematisches Modell Mathematische Physik Differentialgleichung Gewöhnliche Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022641705&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT smithcarlosa afirstcourseindifferentialequationsmodelingandsimulation AT campbellscottw afirstcourseindifferentialequationsmodelingandsimulation |