VisualDSolve: visualizing differential equations with Mathematica
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 271 S. Ill., graph. Darst. 1 Diskette |
| ISBN: | 0387947213 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
PART 1 The VisualDSolve Manual
1 VisualDSolve 3
1.1 Loading the Package 3
1.2 Basic Usage 5
1.3 Options 6
1.4 Setting and Seeing the Initial Values 7
1.5 Style and Accuracy Control 12
1.6 Symbolic Solutions 17
1.7 Direction Fields 20
1.8 Isoclines 21
1.9 Inflection Curves 28
1.10 Controlling the Numerical Method 28
1.11 Using the Output 33
2 Auxiliary Functions 39
2.1 FreehandAttempt 39
2.2 PhaseLine 42
2.3 ResidualPlot 45
2.4 GetPts 50
2.5 ToSystem 50
2.6 ColorParametricPlot 51
2.7 FlowParametricPlot 51
3 SystemSolutionPlot 53
3.1 Basic Usage 53
3.2 Stylish Plots 57
33 Using the Output 60
xii Contents
4 PbasePlot 63
4.1 Basic Usage 64
4.2 Controlling the Style of the Orbits 66
4.3 Direction Fields and Flow Fields 69
4.4 FlowParametricPlot 73
4.5 Controlling the ^ Domain 75
4.6 Varying a Parameter 78
4.7 Nullcline Plots 80
4.8 The Real Orbit Graph in Three Dimensions 91
4.9 Systems of Three or More Equations 91
4.10 Poincare Sections 95
5 SecondOrderPlot 99
5.1 A Single Second Order Equation 99
5.2 The Ups and Downs of a Helium Balloon 105
5.3 Second Order Systems 108
PART 2 VisualDSolye and Differential
Equations Modeling
VisualDSolve and Differential Equations Modeling l13
6 Differential Equations and Mathematica 115
6.1 Rules of Solving and DSolving Equations 115
6.2 Changing Politics: x Moves to the Right 118
6.3 NDSolve 121
7 Some Parachute Experiments 123
7.1 VisualDSolve 123
7.2 Modeling a Parachutist 126
7.3 Parachute to the Rescue 128
7.4 Infinite Jerk Strikes Again: Dead Body Hits Ground! 130
8 Linear Systems 133
8.1 A Comprehensive View of the Two Dimensional Case 134
8.2 Physical Application: Springs 136
8.3 A Four Dimensional Example 140
9 Logistic Models of Population Growth 145
9.1 One Population 146
9.2 Two Populations 149
Contents xlii
10 Hamiltonian Systems 153
10.1 An Example 153
10.2 An Ideal Pendulum 158
10.3 Higher Dimensions 160
// A Devilish Equation 163
11.1 Skepticism Rewarded I63
11.2 What s Going On 168
12 Lead Flow in the Human Body 171
12.1 The Model 171
12.2 Getting the Lead Out 174
13 Making a Discus Fly 179
13.1 The Model 179
13.2 Drag and Lift 181
133 Implementing the Equations 182
13 4 The Best Throwing Angles 184
14 A Double Pendulum 187
14.1 Shoulder to Elbow 188
14.2 Linearization 193
14.3 Bringing the Pendulum to Life 195
14.4 Chaos, and What Happens on the Way 196
14.5 Synchronized Swinging 200
15 The Duffing Equation 203
151 A Stable Example 203
152 The General Duffing Equation 208
15.3 Flying Duffing Circles 212
15.4 Forced Attraction 216
15.5 What To Do? 217
16 TheTetrapodsqfWada 221
16.1 A Damped, Forced Pendulum 222
16.2 Finding the Cycles 223
16.3 Surprising Periodicity 226
16.4 The Tetrapod 230
16.5 The Curve Drawing Algorithm 237
xiv Contents
17 I Tossed a Book into the Air ... 241
17.1 Euler s Equations 242
17.2 Ellipsoids and the Conservation Laws 248
17.3 Spinning a Book 251
17.4 Rolling the Poinsot Ellipsoid 254
Appendix: Usage Messages 257
References 265
Index 267
Index of VisualDSolve Functions 267
Index of Mathematica Objects 269
Subject Index 271
I
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| any_adam_object | 1 |
| author | Schwalbe, Dan Wagon, Stan |
| author_facet | Schwalbe, Dan Wagon, Stan |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352/0113668 |
| dewey-search | 515/.352/0113668 |
| dewey-sort | 3515 3352 6113668 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV011420307 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:26Z |
| institution | BVB |
| isbn | 0387947213 |
| language | English |
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| physical | XIV, 271 S. Ill., graph. Darst. 1 Diskette |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| spelling | Schwalbe, Dan Verfasser aut VisualDSolve visualizing differential equations with Mathematica Dan Schwalbe ; Stan Wagon New York [u.a.] Springer 1997 XIV, 271 S. Ill., graph. Darst. 1 Diskette txt rdacontent n rdamedia nc rdacarrier Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Visualisierung (DE-588)4188417-6 gnd rswk-swf VisualDSolve (DE-588)4449285-6 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Visualisierung (DE-588)4188417-6 s Mathematica Programm (DE-588)4268208-3 s DE-604 VisualDSolve (DE-588)4449285-6 s Wagon, Stan Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007678137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwalbe, Dan Wagon, Stan VisualDSolve visualizing differential equations with Mathematica Differentialgleichung (DE-588)4012249-9 gnd Mathematica Programm (DE-588)4268208-3 gnd Visualisierung (DE-588)4188417-6 gnd VisualDSolve (DE-588)4449285-6 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4268208-3 (DE-588)4188417-6 (DE-588)4449285-6 |
| title | VisualDSolve visualizing differential equations with Mathematica |
| title_auth | VisualDSolve visualizing differential equations with Mathematica |
| title_exact_search | VisualDSolve visualizing differential equations with Mathematica |
| title_full | VisualDSolve visualizing differential equations with Mathematica Dan Schwalbe ; Stan Wagon |
| title_fullStr | VisualDSolve visualizing differential equations with Mathematica Dan Schwalbe ; Stan Wagon |
| title_full_unstemmed | VisualDSolve visualizing differential equations with Mathematica Dan Schwalbe ; Stan Wagon |
| title_short | VisualDSolve |
| title_sort | visualdsolve visualizing differential equations with mathematica |
| title_sub | visualizing differential equations with Mathematica |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Mathematica Programm (DE-588)4268208-3 gnd Visualisierung (DE-588)4188417-6 gnd VisualDSolve (DE-588)4449285-6 gnd |
| topic_facet | Differentialgleichung Mathematica Programm Visualisierung VisualDSolve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007678137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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