An introduction to ordinary differential equations:
This textbook provides a rigorous & lucid introduction to the theory of ordinary differential equations, which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Summary: | This textbook provides a rigorous & lucid introduction to the theory of ordinary differential equations, which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines. |
| Physical Description: | XII, 321 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387712758 0387712755 ebook 9780387712765 |
Staff View
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| 245 | 1 | 0 | |a An introduction to ordinary differential equations |c Ravi P. Agarwal ; Donal O'Regan |
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Record in the Search Index
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| adam_text | Contents
Preface
vii
1.
Introduction
1
2.
Historical Notes
7
3.
Exact Equations
13
4.
Elementary First-Order Equations
21
5.
First-Order Linear Equations
28
6.
Second-Order Linear Equations
35
7.
Preliminaries to Existence and Uniqueness of Solutions
45
8.
Picard s Method of Successive Approximations
53
9.
Existence Theorems
61
10.
Uniqueness Theorems
68
11.
Differential Inequalities
77
12.
Continuous Dependence on Initial Conditions
84
13.
Preliminary Results from Algebra and Analysis
91
14.
Preliminary Results from Algebra and Analysis (Contd.)
97
15.
Existence and Uniqueness of Solutions of Systems
103
16.
Existence and Uniqueness of Solutions of Systems (Contd.)
109
17.
General Properties of Linear Systems
116
18.
Fundamental Matrix Solution
124
19.
Systems with Constant Coefficients
133
20.
Periodic Linear Systems
144
xii Contents
21.
Asymptotic Behavior of Solutions of Linear Systems
152
22.
Asymptotic Behavior of Solutions of Linear Systems (Contd.)
159
23.
Preliminaries to Stability of Solutions
168
24.
Stability of Quasi-Linear Systems
175
25.
Two-Dimensional Autonomous Systems
181
26.
Two-Dimensional Autonomous Systems (Contd.)
187
27.
Limit Cycles and Periodic Solutions
196
28.
Lyapunov s Direct Method for Autonomous Systems
204
29.
Lyapunov s Direct Method for Nonautonomous Systems
211
30.
Higher-Order Exact and Adjoint Equations
217
31.
Oscillatory Equations
225
32.
Linear Boundary Value Problems
233
33.
Green s Functions
240
34.
Degenerate Linear Boundary Value Problems
250
35.
Maximum Principles
258
36.
Sturm-Liouville Problems
265
37.
Sturm-Liouville Problems (Contd.)
271
38.
Eigenfunction Expansions
279
39.
Eigenfunction Expansions (Contd.)
286
40.
Nonlinear Boundary Value Problems
295
41.
Nonlinear Boundary Value Problems (Contd.)
300
42.
Topics for Further Studies
308
References
315
Index
319
Universitext
Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology,
Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His
research interests include numerical analysis, inequalities, fixed point theorems, and differ¬
ential and difference equations. He is the author/co-author of over
800
journal articles and
more than
20
books, and actively contributes to over
40
journals and book series in various
capacities.
Donai O Regan
received his Ph.D. in mathematics from Oregon State University, Oregon,
U.S.A. He is a professor of mathematics at the National University of Ireland, Galway. He is
the author/co-author of
14
books and has published over
650
papers on fixed point theory,
operator, integral, differential and difference equations. He serves on the editorial board of
many mathematical journals.
Previously, the authors have co-authored/co-edited the following books with Springer:
Infinite Interval Problems for Differential, Difference and Integral Equations; Singular
Differential and Integral Equations with Applications; Nonlinear Analysis and Applications: To
V. Lakshmikanthan on his 80th Birthday. In addition, they have collaborated with others on
the following titles: Positive Solutions of Differential, Difference and Integral Equations;
Oscillation Theory for Difference and Functional Differential Equations; Oscillation Theory for
Second Order Linear, Half-Linear,
Superlinear
and
Sublinear
Dynamic Equations.
An Introduction to Ordinary Differential Equations
This textbook provides a rigorous and lucid introduction to the theory of ordinary
differential equations (ODEs), which serve as mathematical models for many exciting
real-world problems in science, engineering, and other disciplines.
Key Features of this textbook:
•
Effectively organizes the subject into easily manageable sections in the form of
42
class-tested lectures
•
Provides a theoretical treatment by organizing the material around theorems and
proofs
•
Uses detailed examples to drive the presentation
•
Includes numerous exercise sets that encourage pursuing extensions of the materi¬
al, each with an answers or hints section
•
Covers an array of advanced topics which allow for flexibility in developing the sub¬
ject beyond the basics
•
Provides excellent grounding and inspiration for future research contributions to
the field of ODEs and related areas
This book is ideal for a senior undergraduate or a graduate-level course on ordinary
differential equations. Prerequisites include a course in calculus.
|
| adam_txt |
Contents
Preface
vii
1.
Introduction
1
2.
Historical Notes
7
3.
Exact Equations
13
4.
Elementary First-Order Equations
21
5.
First-Order Linear Equations
28
6.
Second-Order Linear Equations
35
7.
Preliminaries to Existence and Uniqueness of Solutions
45
8.
Picard's Method of Successive Approximations
53
9.
Existence Theorems
61
10.
Uniqueness Theorems
68
11.
Differential Inequalities
77
12.
Continuous Dependence on Initial Conditions
84
13.
Preliminary Results from Algebra and Analysis
91
14.
Preliminary Results from Algebra and Analysis (Contd.)
97
15.
Existence and Uniqueness of Solutions of Systems
103
16.
Existence and Uniqueness of Solutions of Systems (Contd.)
109
17.
General Properties of Linear Systems
116
18.
Fundamental Matrix Solution
124
19.
Systems with Constant Coefficients
133
20.
Periodic Linear Systems
144
xii Contents
21.
Asymptotic Behavior of Solutions of Linear Systems
152
22.
Asymptotic Behavior of Solutions of Linear Systems (Contd.)
159
23.
Preliminaries to Stability of Solutions
168
24.
Stability of Quasi-Linear Systems
175
25.
Two-Dimensional Autonomous Systems
181
26.
Two-Dimensional Autonomous Systems (Contd.)
187
27.
Limit Cycles and Periodic Solutions
196
28.
Lyapunov's Direct Method for Autonomous Systems
204
29.
Lyapunov's Direct Method for Nonautonomous Systems
211
30.
Higher-Order Exact and Adjoint Equations
217
31.
Oscillatory Equations
225
32.
Linear Boundary Value Problems
233
33.
Green's Functions
240
34.
Degenerate Linear Boundary Value Problems
250
35.
Maximum Principles
258
36.
Sturm-Liouville Problems
265
37.
Sturm-Liouville Problems (Contd.)
271
38.
Eigenfunction Expansions
279
39.
Eigenfunction Expansions (Contd.)
286
40.
Nonlinear Boundary Value Problems
295
41.
Nonlinear Boundary Value Problems (Contd.)
300
42.
Topics for Further Studies
308
References
315
Index
319
Universitext
Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology,
Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His
research interests include numerical analysis, inequalities, fixed point theorems, and differ¬
ential and difference equations. He is the author/co-author of over
800
journal articles and
more than
20
books, and actively contributes to over
40
journals and book series in various
capacities.
Donai O'Regan
received his Ph.D. in mathematics from Oregon State University, Oregon,
U.S.A. He is a professor of mathematics at the National University of Ireland, Galway. He is
the author/co-author of
14
books and has published over
650
papers on fixed point theory,
operator, integral, differential and difference equations. He serves on the editorial board of
many mathematical journals.
Previously, the authors have co-authored/co-edited the following books with Springer:
Infinite Interval Problems for Differential, Difference and Integral Equations; Singular
Differential and Integral Equations with Applications; Nonlinear Analysis and Applications: To
V. Lakshmikanthan on his 80th Birthday. In addition, they have collaborated with others on
the following titles: Positive Solutions of Differential, Difference and Integral Equations;
Oscillation Theory for Difference and Functional Differential Equations; Oscillation Theory for
Second Order Linear, Half-Linear,
Superlinear
and
Sublinear
Dynamic Equations.
An Introduction to Ordinary Differential Equations
This textbook provides a rigorous and lucid introduction to the theory of ordinary
differential equations (ODEs), which serve as mathematical models for many exciting
real-world problems in science, engineering, and other disciplines.
Key Features of this textbook:
•
Effectively organizes the subject into easily manageable sections in the form of
42
class-tested lectures
•
Provides a theoretical treatment by organizing the material around theorems and
proofs
•
Uses detailed examples to drive the presentation
•
Includes numerous exercise sets that encourage pursuing extensions of the materi¬
al, each with an "answers or hints" section
•
Covers an array of advanced topics which allow for flexibility in developing the sub¬
ject beyond the basics
•
Provides excellent grounding and inspiration for future research contributions to
the field of ODEs and related areas
This book is ideal for a senior undergraduate or a graduate-level course on ordinary
differential equations. Prerequisites include a course in calculus. |
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| id | DE-604.BV023211652 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:12:16Z |
| indexdate | 2024-07-09T21:13:11Z |
| institution | BVB |
| isbn | 9780387712758 0387712755 ebook 9780387712765 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016397707 |
| oclc_num | 181090518 |
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| physical | XII, 321 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Agarwal, Ravi P. 1947- Verfasser (DE-588)112040187 aut An introduction to ordinary differential equations Ravi P. Agarwal ; Donal O'Regan New York, NY Springer 2008 XII, 321 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Universitext This textbook provides a rigorous & lucid introduction to the theory of ordinary differential equations, which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines. Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 O'Regan, Donal Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016397707&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016397707&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Agarwal, Ravi P. 1947- O'Regan, Donal An introduction to ordinary differential equations Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 |
| title | An introduction to ordinary differential equations |
| title_auth | An introduction to ordinary differential equations |
| title_exact_search | An introduction to ordinary differential equations |
| title_exact_search_txtP | An introduction to ordinary differential equations |
| title_full | An introduction to ordinary differential equations Ravi P. Agarwal ; Donal O'Regan |
| title_fullStr | An introduction to ordinary differential equations Ravi P. Agarwal ; Donal O'Regan |
| title_full_unstemmed | An introduction to ordinary differential equations Ravi P. Agarwal ; Donal O'Regan |
| title_short | An introduction to ordinary differential equations |
| title_sort | an introduction to ordinary differential equations |
| topic | Équations différentielles Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Équations différentielles Differential equations Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016397707&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016397707&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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