Ordinary differential equations with applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2006
|
| Series: | Series on applied mathematics
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 244 S. graph. Darst. |
| ISBN: | 9812563199 |
Staff View
MARC
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| 100 | 1 | |a Hsu, Sze-Bi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ordinary differential equations with applications |c Sze-Bi Hsu |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2006 | |
| 300 | |a IX, 244 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on applied mathematics |v 16 | |
| 650 | 4 | |a Ecuaciones diferenciales | |
| 650 | 7 | |a Equações diferenciais ordinárias |2 larpcal | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014712198 | ||
Record in the Search Index
| _version_ | 1804135224114675712 |
|---|---|
| adam_text | Contents
1
INTRODUCTION
1
1.1
Where do ODEs arise
..................... 1
2
FUNDAMENTAL THEORY
9
2.1
Introduction and Preliminaries
................ 9
2.2
Local Existence and Uniqueness of Solutions of I.V.P.
... 12
2.3
Continuation of Solutions
................... 21
2.4
Continuous Dependence Properties
.............. 24
2.5
Differentiability of Initial Conditions and Parameters
.... 27
2.6
Differential Inequalities
.................... 31
2.7
Exercises
............................ 35
3
LINEAR SYSTEMS
41
3.1
Introduction
........................... 41
3.2
Fundamental Matrices
..................... 42
3.3
Linear Systems with Constant Coefficients
.......... 46
3.4
Two-Dimensional Linear Autonomous Systems
....... 55
3.5
Linear Systems with Periodic Coefficients
.......... 59
3.6
Adjoint Systems
........................ 67
3.7
Exercises
............................ 71
4
STABILITY OF NONLINEAR SYSTEMS
77
4.1
Definitions
............................ 77
4.2
Linearization
.......................... 79
4.3
Saddle Point Property: Stable and Unstable Manifolds
... 88
4.4
Orbital Stability
........................ 99
4.5
Travelling Wave Solutions
................... 106
4.6
Exercises
............................ 114
vi
. CONTENTS
5
METHOD OF LYAPUNOV FUNCTIONS
117
5.1
An Introduction to Dynamical Systems
........... 117
5.2
Lyapunov Functions [H]
.................... 124
5.3
Simple Oscillatory Phenomena: [H]
.............. 135
5.4
Exercises
............................ 138
6
TWO-DIMENSIONAL SYSTEMS
143
6.1
Poincaré-Bendixson
Theorem
................. 143
6.2
Levinson-Smith Theorem
................... 154
6.3 Hopf
Bifurcation
........................ 163
6.4
Exercises
............................ 168
7
SECOND ORDER LINEAR EQUATIONS
171
7.1
Sturm s Comparison and Sturm-Liouville Boundary Value
Problems
............................ 171
7.2
Distributions
.......................... 179
7.3
Green s Function
........................ 181
7.4
Fredholm
Alternative for
2nd
Order Linear Equations
. . . 187
7.5
Exercises
............................ 189
8
THE INDEX THEORY AND
BROUWER
DEGREE
193
8.1
Index Theory in the Plane
................... 193
8.2
Introduction to the
Brouwer
Degree in
Лп
.......... 202
8.3
Exercises
............................ 206
9
INTRODUCTION TO PERTURBATION METHODS
209
9.1
Regular Perturbation Methods
................ 209
9.2
Singular Perturbations
:
Boundary Value Problems
..... 216
9.3
Singular Perturbation
:
Initial Value Problems
....... 221
9.4
Exercises
............................ 234
BIBLIOGRAPHY
237
INDEX
241
|
| adam_txt |
Contents
1
INTRODUCTION
1
1.1
Where do ODEs arise
. 1
2
FUNDAMENTAL THEORY
9
2.1
Introduction and Preliminaries
. 9
2.2
Local Existence and Uniqueness of Solutions of I.V.P.
. 12
2.3
Continuation of Solutions
. 21
2.4
Continuous Dependence Properties
. 24
2.5
Differentiability of Initial Conditions and Parameters
. 27
2.6
Differential Inequalities
. 31
2.7
Exercises
. 35
3
LINEAR SYSTEMS
41
3.1
Introduction
. 41
3.2
Fundamental Matrices
. 42
3.3
Linear Systems with Constant Coefficients
. 46
3.4
Two-Dimensional Linear Autonomous Systems
. 55
3.5
Linear Systems with Periodic Coefficients
. 59
3.6
Adjoint Systems
. 67
3.7
Exercises
. 71
4
STABILITY OF NONLINEAR SYSTEMS
77
4.1
Definitions
. 77
4.2
Linearization
. 79
4.3
Saddle Point Property: Stable and Unstable Manifolds
. 88
4.4
Orbital Stability
. 99
4.5
Travelling Wave Solutions
. 106
4.6
Exercises
. 114
vi
. CONTENTS
5
METHOD OF LYAPUNOV FUNCTIONS
117
5.1
An Introduction to Dynamical Systems
. 117
5.2
Lyapunov Functions [H]
. 124
5.3
Simple Oscillatory Phenomena: [H]
. 135
5.4
Exercises
. 138
6
TWO-DIMENSIONAL SYSTEMS
143
6.1
Poincaré-Bendixson
Theorem
. 143
6.2
Levinson-Smith Theorem
. 154
6.3 Hopf
Bifurcation
. 163
6.4
Exercises
. 168
7
SECOND ORDER LINEAR EQUATIONS
171
7.1
Sturm's Comparison and Sturm-Liouville Boundary Value
Problems
. 171
7.2
Distributions
. 179
7.3
Green's Function
. 181
7.4
Fredholm
Alternative for
2nd
Order Linear Equations
. . . 187
7.5
Exercises
. 189
8
THE INDEX THEORY AND
BROUWER
DEGREE
193
8.1
Index Theory in the Plane
. 193
8.2
Introduction to the
Brouwer
Degree in
Лп
. 202
8.3
Exercises
. 206
9
INTRODUCTION TO PERTURBATION METHODS
209
9.1
Regular Perturbation Methods
. 209
9.2
Singular Perturbations
:
Boundary Value Problems
. 216
9.3
Singular Perturbation
:
Initial Value Problems
. 221
9.4
Exercises
. 234
BIBLIOGRAPHY
237
INDEX
241 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T14:13:51Z |
| indexdate | 2024-07-09T20:37:06Z |
| institution | BVB |
| isbn | 9812563199 |
| language | English |
| lccn | 2005044280 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014712198 |
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| physical | IX, 244 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on applied mathematics |
| series2 | Series on applied mathematics |
| spelling | Hsu, Sze-Bi Verfasser aut Ordinary differential equations with applications Sze-Bi Hsu New Jersey [u.a.] World Scientific 2006 IX, 244 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on applied mathematics 16 Ecuaciones diferenciales Equações diferenciais ordinárias larpcal Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Series on applied mathematics 16 (DE-604)BV007228284 16 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014712198&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsu, Sze-Bi Ordinary differential equations with applications Series on applied mathematics Ecuaciones diferenciales Equações diferenciais ordinárias larpcal Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 |
| title | Ordinary differential equations with applications |
| title_auth | Ordinary differential equations with applications |
| title_exact_search | Ordinary differential equations with applications |
| title_exact_search_txtP | Ordinary differential equations with applications |
| title_full | Ordinary differential equations with applications Sze-Bi Hsu |
| title_fullStr | Ordinary differential equations with applications Sze-Bi Hsu |
| title_full_unstemmed | Ordinary differential equations with applications Sze-Bi Hsu |
| title_short | Ordinary differential equations with applications |
| title_sort | ordinary differential equations with applications |
| topic | Ecuaciones diferenciales Equações diferenciais ordinárias larpcal Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Ecuaciones diferenciales Equações diferenciais ordinárias Équations différentielles Differential equations Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014712198&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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