Differential equations: introduction and qualitative theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1994
|
| Ausgabe: | 2. ed., rev. and expanded |
| Schriftenreihe: | Pure and applied mathematics
180 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 3. Aufl. u.d.T.: Cronin, Jane: Ordinary differential equations |
| Beschreibung: | XI, 370 S. graph. Darst. |
| ISBN: | 0824791894 |
Internformat
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| 245 | 1 | 0 | |a Differential equations |b introduction and qualitative theory |c Jane Cronin |
| 250 | |a 2. ed., rev. and expanded | ||
| 264 | 1 | |a New York u.a. |b Dekker |c 1994 | |
| 300 | |a XI, 370 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 180 | |
| 500 | |a 3. Aufl. u.d.T.: Cronin, Jane: Ordinary differential equations | ||
| 650 | 7 | |a Equacoes diferenciais |2 larpcal | |
| 650 | 4 | |a Differential equations | |
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Datensatz im Suchindex
| _version_ | 1804123974285656064 |
|---|---|
| adam_text | Contents
Preface to Second Edition iii
Preface to First Edition v
Chapter 0. Introduction 1
Chapter 1. Existence Theorems 5
What This Chapter Is About 5
Existence Theorem by Successive Approximations 7
Differentiability Theorem 23
Existence Theorem for Equation With a Parameter 26
Existence Theorem Proved by Using a Contraction
Mapping 28
Existence Theorem Without Uniqueness 33
Extension Theorems 46
Exercises for Chapter 1 51
Examples 55
Chapter 2. Linear Systems 65
Existence Theorems for Linear Systems 65
Homogeneous Linear Equations: General Theory 70
Homogeneous Linear Equations With Constant
Coefficients 77
Homogeneous Linear Equations With Periodic
Coefficients: Floquet Theory 93
Inhomogeneous Linear Equations 105
Sturm Liouville Theory 107
Exercises for Chapter 2 121
ix
x Contents
Chapter 3. Autonomous Systems 127
General Properties of Solutions of Autonomous Systems 127
Orbits Near an Equilibrium Point: The Two
Dimensional Case 139
Exercises for Chapter 3 157
Chapter 4. Stability 161
Introduction 161
Definition of Stability 162
Examples 165
Stability of Solutions of Linear Systems 167
Stability of Solutions of Nonlinear Systems 174
Some Stability Theory for Autonomous Nonlinear Systems 183
Exercises for Chapter 4 195
Chapter 5. The Lyapunov Second Method 197
Definition of Lyapunov Function 197
Theorems of the Lyapunov Second Method 200
Application of the Second Method 211
Exercises for Chapter 5 215
Chapter 6. Periodic Solutions 217
Introduction 217
Poincare Bendixson Theorem 218
Application of the Poincare Bendixson Theorem 232
Stable Periodic Solutions in the n Dimensional Case 241
Periodic Solutions for Nonautonomous Systems 254
Exercises for Chapter 6 258
Chapter 7. Bifurcation and Branching of
Periodic Solutions 261
Introduction 261
A. Branching of Periodic Solutions 262
An Example 262
Existence of Periodic Solutions 264
Stability of the Periodic Solutions 279
Generalization of Malkin s Theorem 287
Contents xi
Examples of Branching of Periodic Solutions 294
B. Bifurcation of Periodic Solutions 298
The General Problem and a Partial Solution to It 298
The Hopf Bifurcation Theorem 310
A Bifurcation Theorem Based on Sell s Theorem 314
Exercises for Chapter 7 315
Appendix 321
Ascoli s Theorem 321
Principle of Contraction Mappings 321
Topological Degree 323
References 357
Index 365
|
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| discipline | Mathematik |
| edition | 2. ed., rev. and expanded |
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| id | DE-604.BV009634482 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:17Z |
| institution | BVB |
| isbn | 0824791894 |
| language | English |
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| physical | XI, 370 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Cronin, Jane 1922-2018 Verfasser (DE-588)122430166 aut Differential equations introduction and qualitative theory Jane Cronin 2. ed., rev. and expanded New York u.a. Dekker 1994 XI, 370 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 180 3. Aufl. u.d.T.: Cronin, Jane: Ordinary differential equations Equacoes diferenciais larpcal Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Pure and applied mathematics 180 (DE-604)BV000001885 180 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006367029&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 |
| spellingShingle | Cronin, Jane 1922-2018 Differential equations introduction and qualitative theory Pure and applied mathematics Equacoes diferenciais larpcal Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4012249-9 |
| title | Differential equations introduction and qualitative theory |
| title_auth | Differential equations introduction and qualitative theory |
| title_exact_search | Differential equations introduction and qualitative theory |
| title_full | Differential equations introduction and qualitative theory Jane Cronin |
| title_fullStr | Differential equations introduction and qualitative theory Jane Cronin |
| title_full_unstemmed | Differential equations introduction and qualitative theory Jane Cronin |
| title_short | Differential equations |
| title_sort | differential equations introduction and qualitative theory |
| title_sub | introduction and qualitative theory |
| topic | Equacoes diferenciais larpcal Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Equacoes diferenciais Differential equations Gewöhnliche Differentialgleichung Differentialgleichung |
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