Ordinary differential equations: example-driven, including Maple Code
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2018]
|
Schriftenreihe: | De Gruyter Graduate
|
Schlagworte: | |
Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110447422&searchTitles=true Inhaltsverzeichnis |
Beschreibung: | XIII, 221 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
ISBN: | 9783110447422 3110447428 |
Internformat
MARC
LEADER | 00000nam a2200000 c 4500 | ||
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024 | 3 | |a 9783110447422 | |
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245 | 1 | 0 | |a Ordinary differential equations |b example-driven, including Maple Code |c Radu Precup |
264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2018] | |
264 | 4 | |c © 2018 | |
300 | |a XIII, 221 Seiten |b Illustrationen, Diagramme |c 24 cm x 17 cm | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 0 | |a De Gruyter Graduate | |
650 | 0 | 7 | |a Maple |g Programm |0 (DE-588)4209397-1 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Algorithmus |0 (DE-588)4001183-5 |2 gnd |9 rswk-swf |
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689 | 0 | 0 | |a Algorithmus |0 (DE-588)4001183-5 |D s |
689 | 0 | 1 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
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Datensatz im Suchindex
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adam_text | CONTENTS
PREFACE * VII
PART I: THEORY
CHAPTER 1 FIRST-ORDER DIFFERENTIAL EQUATIONS * 3
1.1 PRELIMINARIES * 3
1.2 CLASSES OF FIRST-ORDER DIFFERENTIAL EQUATIONS * 6
1.2.1 DIFFERENTIAL EQUATIONS WITH SEPARABLE VARIABLES * 6
1.2.2 DIFFERENTIAL EQUATIONS OF HOMOGENEOUS TYPE * 7
1.2.3 FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS * 8
1.2.4 BERNOULLI EQUATIONS * 13
1.2.5 RICCATI EQUATIONS * 14
1.3 MATHEMATICAL MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS *
1.3.1 RADIOACTIVE DECAY * 15
1.3.2 NEWTON*S LAW OF HEAT TRANSFER
-----
16
1.3.3 CHEMICAL REACTIONS * 17
1.3.4 POPULATION GROWTH OF A SINGLE SPECIES * 18
1.3.5 THE GOMPERTZ EQUATION
-----
20
CHAPTER 2 LINEAR DIFFERENTIAL SYSTEMS * 22
2.1 PRELIMINARIES * 22
2.2 MATHEMATICAL MODELING WITH LINEAR DIFFERENTIAL SYSTEMS * 23
2.3 MATRIX NOTATION FOR SYSTEMS * 26
2.4 SUPERPOSITION PRINCIPLE FOR LINEAR SYSTEMS * 27
2.5 LINEAR DIFFERENTIAL SYSTEMS WITH CONSTANT COEFFICIENTS * 28
2.5.1 THE GENERAL SOLUTION
-----
28
2.5.2 STRUCTURE OF SOLUTION SET FOR HOMOGENEOUS LINEAR SYSTEMS * 31
2.5.3 THE CONCEPT OF FUNDAMENTAL MATRIX * 32
2.5.4 METHOD OF EIGENVALUES AND EIGENVECTORS * 35
2.6 METHOD OF VARIATION OF PARAMETERS * 40
2.7 HIGHER-DIMENSIONAL LINEAR SYSTEMS * 42
2.8 USE OF THE JORDAN CANONICAL FORM OF A MATRIX * 44
2.9 DYNAMIC ASPECTS OF DIFFERENTIAL SYSTEMS * 46
2.10 PRELIMINARIES OF STABILITY * 52
CHAPTER 3 SECOND-ORDER DIFFERENTIAL EQUATIONS * 53
3.1 NEWTON*S SECOND LAW OF MOTION
-----
53
3.2 REDUCTION OF ORDER
-----
54
3.3 EQUIVALENCE TO A FIRST-ORDER SYSTEM * 57
3.4 THE METHOD OF ELIMINATION
-----
58
3.5 LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS * 59
3.5.1 THE SOLUTION SET
-----
59
3.5.2 HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS * 59
3.5.3 VARIATION OF PARAMETERS METHOD * 61
3.5.4 THE METHOD OF UNDETERMINED COEFFICIENTS * 62
3.5.5 EULER EQUATIONS * 64
3.6 BOUNDARY VALUE PROBLEMS * 66
3.7 HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS * 69
CHAPTER 4 NONLINEAR DIFFERENTIAL EQUATIONS * 72
4.1 MATHEMATICAL MODELS EXPRESSED BY NONLINEAR SYSTEMS * 72
4.1.1 THE LOTKA-VOLTERRA MODEL
-----
72
4.1.2 THE SIR EPIDEMIC MODEL
-----
73
4.1.3 AN IMMUNOLOGICAL MODEL * 74
4.1.4 A MODEL IN HEMATOLOGY * 75
4.2 GRONWATL*S INEQUALITY* 75
4.3 UNIQUENESS OF SOLUTIONS FOR THE CAUCHY PROBLEM * 77
4.4 CONTINUOUS DEPENDENCE OF SOLUTIONS ON THE INITIAL VALUES * 81
4.5 THE CAUCHY PROBLEM FOR SYSTEMS * 83
4.6 THE CAUCHY PROBLEM FOR HIGHER-ORDER EQUATIONS * 84
4.7 PERIODIC SOLUTIONS * 85
4.8 PICARD*S METHOD OF SUCCESSIVE APPROXIMATIONS * 88
4.8.1 PICARD*S ITERATION * 88
4.8.2 THE INTERVAL OF PICARD*S ITERATION * 91
4.8.3 CONVERGENCE OF PICARD*S ITERATION * 92
4.9 EXISTENCE OF SOLUTIONS FOR THE CAUCHY PROBLEM * 93
CHAPTER 5 STABILITY OF SOLUTIONS * 97
5.1 THE NOTION OF A STABLE SOLUTION * 97
5.2 STABILITY OF LINEAR SYSTEMS * 99
5.3 STABILITY OF LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS * 100
5.4 STABILITY OF SOLUTIONS OF NONLINEAR SYSTEMS * 101
5.5 METHOD OF LYAPUNOV FUNCTIONS * 106
5.6 GLOBALLY ASYMPTOTICALLY STABLE SYSTEMS * 111
CHAPTER 6 DIFFERENTIAL SYSTEMS WITH CONTROL PARAMETERS * 113
6.1 BIFURCATIONS * 113
6.2 HOPF BIFURCATIONS
-----
115
6.3 OPTIMIZATION OF DIFFERENTIAL SYSTEMS * 119
6.4 DYNAMIC OPTIMIZATION OF DIFFERENTIAL SYSTEMS * 122
PART II: EXERCISES
SEMINAR 1
1.1
1.2
1.3
1.4
CLASSES OF FIRST-ORDER DIFFERENTIAL EQUATIONS
* 127
SOLVED EXERCISES * 127
PROPOSED EXERCISES * 129
SOLUTIONS * 130
PROJECT: PROBLEMS OF GEOMETRY THAT LEAD TO
DIFFERENTIAL EQUATIONS * 131
SEMINAR 2
2.1
2.2
2.3
2.4
MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
* 133
SOLVED EXERCISES * 133
PROPOSED EXERCISES * 135
HINTS AND ANSWERS * 136
PROJECT: INFLUENCE OF EXTERNAL ACTIONS OVER THE EVOLUTION
OF SOME PROCESSES * 136
SEMINAR 3
3.1
3.2
3.3
3.4
LINEAR DIFFERENTIAL SYSTEMS
* 139
SOLVED EXERCISES * 139
PROPOSED EXERCISES * 143
HINTS AND SOLUTIONS * 145
PROJECT: MATHEMATICAL MODELS REPRESENTED BY LINEAR DIFFERENTIAL
SYSTEMS * 146
SEMINAR 4
4.1
4.2
4.3
4.4
SECOND-ORDER DIFFERENTIAL EQUATIONS
* 148
SOLVED EXERCISES * 148
PROPOSED EXERCISES * 150
SOLUTIONS * 151
PROJECT: BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER DIFFERENTIAL
EQUATIONS
-----
152
SEMINAR 5
5.1
5.2
5.3
5.4
CORNWALL S INEQUALITY
*
154
SOLVED EXERCISES * 154
PROPOSED EXERCISES * 157
HINTS AND SOLUTIONS * 157
PROJECT: INTEGRAL AND DIFFERENTIAL INEQUALITIES * 158
SEMINAR 6 METHOD OF SUCCESSIVE APPROXIMATIONS
* 163
6.1
6.2
SOLVED EXERCISES * 163
PROPOSED EXERCISES * 164
6.3 HINTS AND SOLUTIONS * 165
6.4 PROJECT: THE VECTORIAL METHOD FOR THE TREATMENT OF NONLINEAR
DIFFERENTIAL
SYSTEMS * 165
SEMINAR 7 STABILITY OF SOLUTIONS * 170
7.1 SOLVED EXERCISES * 170
7.2 PROPOSED EXERCISES * 172
7.3 HINTS AND SOLUTIONS * 173
7.4 PROJECT: STABLE AND UNSTABLE INVARIANT MANIFOLDS * 173
PART III: MAPLE CODE
LAB
1
INTRODUCTION TO MAPLE
* 179
1.1 NUMERICAL CALCULUS * 179
1.2 SYMBOLIC CALCULUS * 181
LAB
2
DIFFERENTIAL EQUATIONS WITH MAPLE
* 185
2.1 THE DETOOLS PACKAGE * 185
2.2 WORKING THEMES
-----
186
LAB
3
LINEAR DIFFERENTIAL SYSTEMS
* 188
3.1 THE LINALG PACKAGE * 188
3.2 LINEAR DIFFERENTIAL SYSTEMS * 188
3.3 WORKING THEMES * 190
LAB
4
SECOND-ORDER DIFFERENTIAL EQUATIONS
* 191
4.1 SPRING-MASS OSCILLATOR EQUATION WITH MAPLE * 191
4.2 BOUNDARY VALUE PROBLEMS WITH MAPLE * 193
4.3 WORKING THEMES
-----
193
LAB
5
NONLINEAR DIFFERENTIAL SYSTEMS
* 195
5.1 THE LOTKA-VOLTERRA SYSTEM * 195
5.2 A MODEL FROM HEMATOLOGY * 196
5.3 WORKING THEMES * 197
LAB
6
NUMERICAL COMPUTATION OF SOLUTIONS
* 198
6.1 INITIAL VALUE PROBLEMS * 198
6.2 BOUNDARY VALUE PROBLEMS * 199
6.3 WORKING THEMES * 202
LAB 7 WRITING CUSTOM MAPLE PROGRAMS * 204
7.1 METHOD OF SUCCESSIVE APPROXIMATIONS * 204
7.2 EULER*S METHOD
-----
206
7.3 THE SHOOTING METHOD------208
7.4 WORKING THEMES * 211
LAB 8 DIFFERENTIAL SYSTEMS WITH CONTROL PARAMETERS * 212
8.1 BIFURCATIONS * 212
8.2 OPTIMIZATION WITH MAPLE------213
8.3 WORKING THEMES
-----
215
BIBLIOGRAPHY * 217
INDEX * 219
|
any_adam_object | 1 |
author | Precup, Radu 1955- |
author_GND | (DE-588)1028201435 |
author_facet | Precup, Radu 1955- |
author_role | aut |
author_sort | Precup, Radu 1955- |
author_variant | r p rp |
building | Verbundindex |
bvnumber | BV044734374 |
classification_rvk | SK 520 |
ctrlnum | (OCoLC)1024117672 (DE-599)DNB1078861226 |
dewey-full | 510 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 510 - Mathematics |
dewey-raw | 510 |
dewey-search | 510 |
dewey-sort | 3510 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV044734374 |
illustrated | Illustrated |
indexdate | 2024-07-10T08:00:42Z |
institution | BVB |
institution_GND | (DE-588)10095502-2 |
isbn | 9783110447422 3110447428 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030130376 |
oclc_num | 1024117672 |
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owner_facet | DE-19 DE-BY-UBM DE-29T DE-355 DE-BY-UBR DE-20 DE-634 DE-83 DE-703 |
physical | XIII, 221 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
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spelling | Precup, Radu 1955- Verfasser (DE-588)1028201435 aut Ordinary differential equations example-driven, including Maple Code Radu Precup Berlin ; Boston De Gruyter [2018] © 2018 XIII, 221 Seiten Illustrationen, Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Maple Programm (DE-588)4209397-1 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Fachhochschul-/Hochschulausbildung Algorithmus (DE-588)4001183-5 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Maple Programm (DE-588)4209397-1 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-044744-6 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-044750-7 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110447422&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030130376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Precup, Radu 1955- Ordinary differential equations example-driven, including Maple Code Maple Programm (DE-588)4209397-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Algorithmus (DE-588)4001183-5 gnd |
subject_GND | (DE-588)4209397-1 (DE-588)4020929-5 (DE-588)4001183-5 |
title | Ordinary differential equations example-driven, including Maple Code |
title_auth | Ordinary differential equations example-driven, including Maple Code |
title_exact_search | Ordinary differential equations example-driven, including Maple Code |
title_full | Ordinary differential equations example-driven, including Maple Code Radu Precup |
title_fullStr | Ordinary differential equations example-driven, including Maple Code Radu Precup |
title_full_unstemmed | Ordinary differential equations example-driven, including Maple Code Radu Precup |
title_short | Ordinary differential equations |
title_sort | ordinary differential equations example driven including maple code |
title_sub | example-driven, including Maple Code |
topic | Maple Programm (DE-588)4209397-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Algorithmus (DE-588)4001183-5 gnd |
topic_facet | Maple Programm Gewöhnliche Differentialgleichung Algorithmus |
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