Modelling with ordinary differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press
1993
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 285 S. graph. Darst. |
| ISBN: | 0849386365 |
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Datensatz im Suchindex
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| adam_text | IMAGE 1
MODELIMG WITH
ORDINARY DIFFERENTIAL EQUATIONS
T.P. DREYER DEPARTMENT OF APPLIED MATHEMATICS UNIVERSITY OF STELLENBOSCH
STELLENBOSCH, SOUTH AFRICA
(G)
CRC PRESS BOCA RATON ANN ARBOR LONDON TOKYO
IMAGE 2
- CONTENTS
PREFACE
1 I N T R O D U C T I ON 1
1.1 MATHEMATICAL MODELLING 1
1.2 BOUNDARY VALUE PROBLEMS 3
1.3 DIRECTION FIELDS 7
1.4 FINDING ZEROS 13
1.5 EXERCISES 20
2 F I R ST O R D ER DIFFERENTIAL E Q U A T I O NS 23
2.1 INTRODUCTION 23
2.2 POPULATION GROWTH: MALTHUS MODEL 29
2.3 LEAST SQUARES METHOD OF CURVE FITTING 33
2.4 POPULATION GROWTH: LOGISTIC MODEL 37
2.5 HARVESTING 45
2.6 OPTIMIZATION OF PROFIT 50
2.7 EPIDEMICS 54
2.8 P O T A TO BLIGHT 56
2.9 FREE FALL WITH AIR RESISTANCE 60
2.10 POWER 67
2.11 ROCKETS 70
2.12 EXERCISES 75
2.13 PROJECTS 84
2.14 MATHEMATICAL BACKGROUND 92
3 N U M E R I C AL M E T H O DS 99
3.1 INTRODUCTION 99
3.2 EXISTENCE THEOREM 100
3.3 EULER ALGORITHM 102
IMAGE 3
3.4 ERROR ANALYSIS 105
3.5 R U N G E - K U T TA ALGORITHM 112
3.6 FRUITFLIES 116
3.7 EXERCISES 121
3.8 PROJECTS 125
3.9 MATHEMATICAL BACKGROUND 127
4 L A P L A CE T R A N S F O R MS 1 33
4.1 LINEAR TRANSFORMS 133
4.2 SOME PROPERTIES OF LAPLACE TRANSFORMS 136
4.3 SOLVING DIFFERENTIAL EQUATIONS WITH LAPLACE TRANSFORMS . . 141
4.4 TABLE OF LAPLACE TRANSFORMS 148
4.5 EXERCISES 150
4.6 PROJECTS 153
4.7 MATHEMATICAL BACKGROUND 154
5 S I I I I U L T A N E O US L I N E AR F I R ST O R D ER D I F F E R E
N T I AL E Q U A T I O NS 1 65
5.1 INTRODUCTION 165
5.2 PROJECTILE TRAJECTORIES WITH AIR RESISTANCE 168
5.3 ROMANTIC RELATIONSHIPS 171
5.4 NEUTRON FLOW 176
5.5 ELECTRICAL NETWORKS 180
5.6 MARRIAGE 187
5.7 RESIDENTIAL SEGREGATION 188
5.8 EXERCISES 192
5.9 PROJECTS 193
5.10 MATHEMATICAL BACKGROUND 200
6 S E C O ND O R D ER LINEAR DIFFERENTIAL E Q U A T I O NS 2 05
6.1 MECHANICAL VIBRATIONS 205
6.2 ELECTRICAL NETWORKS 221
IMAGE 4
6.3 T HE IGNITION OF AN AUTOMOBILE 223
6.4 SIMULTANEOUS EQUATIONS 228
6.5 EXERCISES 231
6.6 PROJECTS 233
6.7 MATHEMATICAL BACKGROUND 235
7 S E C O ND O R D ER N O I I L I N E AR D I F F E R E N T I AL E Q U A
T I O NS 2 37
7.1 INTRODUCTION 237
7.2 T HE PENDIILUM WITHOUT DAMPING 239
7.3 T HE PENDIILUM WITH DAMPING 248
7.4 POPULATION OF INTERACTING SPECIES 252
7.5 EXERCISES 260
7.6 MATHEMATICAL BACKGROUND 262
8 T A B LE OF I N T E G R A LS 2 63
9 A N S W E RS 2 67
10 R E F E R E N C ES 2 77
INDEX 282
|
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| id | DE-604.BV008408544 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:19:14Z |
| institution | BVB |
| isbn | 0849386365 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005538378 |
| oclc_num | 260142933 |
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| physical | 285 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Dreyer, T. P. Verfasser aut Modelling with ordinary differential equations T. P. Dreyer Boca Raton, Fla. [u.a.] CRC Press 1993 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Gewone differentiaalvergelijkingen gtt Modèles mathématiques Wiskundige modellen gtt Équations différentielles Mathematisches Modell Differential equations Mathematical models Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s Differentialgleichung (DE-588)4012249-9 s DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Modellierung (DE-588)4170297-9 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005538378&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dreyer, T. P. Modelling with ordinary differential equations Gewone differentiaalvergelijkingen gtt Modèles mathématiques Wiskundige modellen gtt Équations différentielles Mathematisches Modell Differential equations Mathematical models Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Modellierung (DE-588)4170297-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4012249-9 (DE-588)4170297-9 (DE-588)4114528-8 |
| title | Modelling with ordinary differential equations |
| title_auth | Modelling with ordinary differential equations |
| title_exact_search | Modelling with ordinary differential equations |
| title_full | Modelling with ordinary differential equations T. P. Dreyer |
| title_fullStr | Modelling with ordinary differential equations T. P. Dreyer |
| title_full_unstemmed | Modelling with ordinary differential equations T. P. Dreyer |
| title_short | Modelling with ordinary differential equations |
| title_sort | modelling with ordinary differential equations |
| topic | Gewone differentiaalvergelijkingen gtt Modèles mathématiques Wiskundige modellen gtt Équations différentielles Mathematisches Modell Differential equations Mathematical models Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Modellierung (DE-588)4170297-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Gewone differentiaalvergelijkingen Modèles mathématiques Wiskundige modellen Équations différentielles Mathematisches Modell Differential equations Mathematical models Gewöhnliche Differentialgleichung Differentialgleichung Modellierung |
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