Ordinary differential equations with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey u.a.
World Scientific
2013
|
| Edition: | 2. ed. |
| Series: | Series on applied mathematics
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 297 S. graph. Darst. |
| ISBN: | 9789814452908 |
Staff View
MARC
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| 245 | 1 | 0 | |a Ordinary differential equations with applications |c Sze-Bi Hsu |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey u.a. |b World Scientific |c 2013 | |
| 300 | |a XIII, 297 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 21 | |
| 500 | |a Includes bibliographical references and index | ||
| 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:BVB01-026129261 | ||
Record in the Search Index
| _version_ | 1804150557197205504 |
|---|---|
| adam_text | Contents
Preface
to the First Edition
v
Preface to the Second Edition
ix
1.
INTRODUCTION
1
1.1
Where do ODEs arise
.................... 1
2.
FUNDAMENTAL THEORY
11
2.1
Introduction and Preliminaries
............... 11
2.2
Local Existence and Uniqueness of Solutions of I.V.P.
. . 14
2.3
Continuation of Solutions
.................. 23
2.4
Continuous Dependence Properties
............. 26
2.5
Differentiability of I.C. and Parameters
.......... 29
2.6
Differential Inequalities
................... 32
2.7
Exercises
........................... 37
3.
LINEAR SYSTEMS
43
3.1
Introduction
.......................... 43
3.2
Fundamental Matrices
.................... 44
3.3
Linear Systems with Constant Coefficients
......... 49
3.4
Two-Dimensional Linear Autonomous Systems
...... 58
3.5
Linear Systems with Periodic Coefficients
......... 62
3.6
Adjoint Systems
....................... 70
3.7
Exercises
........................... 74
4.
STABILITY OF NONLINEAR SYSTEMS
81
4.1
Definitions
........................... 81
Xl
xii
ORDINARY DIFFERENTIAL EQUATIONS WITH APPLICATIONS
4.2
Linearization
......................... 83
4.3
Saddle Point Property
.................... 92
4.4
Orbital Stability
....................... 102
4.5
Travelling Wave Solutions
.................. 110
4.6
Exercises
........................... 117
5.
METHOD OF LYAPUNOV FUNCTIONS
123
5.1
An Introduction to Dynamical Systems
.......... 123
5.2
Lyapunov Functions
..................... 130
5.3
Simple Oscillatory Phenomena
............... 142
5.4
Gradient Vector Fields
.................... 145
5.5
Exercises
........................... 147
6.
TWO-DIMENSIONAL SYSTEMS
157
6.1
Poincaré-Bendixson
Theorem
................ 157
6.2
Levinson-Smith Theorem
.................. 168
6.3 Hopf
Bifurcation
....................... 177
6.4
Exercises
........................... 183
7.
SECOND ORDER LINEAR EQUATIONS
189
7.1
Sturm s Comparison Theorem and Sturm-Liouville
В
VP .
189
7.2
Distributions
......................... 197
7.3
Green s Function
....................... 199
7.4 Fredhohn
Alternative
..................... 206
7.5
Exercises
........................... 209
8.
THE INDEX THEORY AND
BROUWER
DEGREE
213
8.1
Index Theory in the Plane
.................. 213
8.2
Introduction to the
Brouwer
Degree in R
......... 221
8.3
Exercises
........................... 226
9.
PERTURBATION METHODS
229
9.1
Regular Perturbation Methods
............... 229
9.2
Singular Perturbation
:
Boundary Value Problem
..... 235
9.3
Singular Perturbation
:
Initial Value Problem
....... 241
9.4
Exercises
........................... 253
10.
INTRODUCTION TO MONOTONE DYNAMICAL SYSTEMS
255
Contents xiii
10.1 Monotone
Dynamical
System
with
Applications
to Coop¬
erative
Systems
and Competitive Systems
......... 255
10.2
Uniform Persistence
..................... 261
10.3
Application
:
Competition of Two Species in a Chemostat
with Inhibition
........................ 270
10.4
Two Species Competition Models
.............. 282
10.5
Exercises
........................... 286
Bibliography
291
Index
295
|
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| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)859373592 (DE-599)BVBBV041153849 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV041153849 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:49Z |
| institution | BVB |
| isbn | 9789814452908 |
| language | English |
| lccn | 2013010520 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026129261 |
| oclc_num | 859373592 |
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| owner | DE-703 DE-188 DE-384 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-188 DE-384 DE-19 DE-BY-UBM |
| physical | XIII, 297 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on applied mathematics |
| series2 | Series on applied mathematics |
| spelling | Hsu, Sze-Bi 1948- Verfasser (DE-588)173629903 aut Ordinary differential equations with applications Sze-Bi Hsu 2. ed. New Jersey u.a. World Scientific 2013 XIII, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on applied mathematics 21 Includes bibliographical references and index Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Series on applied mathematics 21 (DE-604)BV007228284 21 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsu, Sze-Bi 1948- Ordinary differential equations with applications Series on applied mathematics 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_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 | Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007228284 |
| work_keys_str_mv | AT hsuszebi ordinarydifferentialequationswithapplications |