An introduction to ordinary differential equations / Ravi P. Agarwal, Donal O'Regan.

Format:

Book

Author/Creator:

Agarwal, Ravi P.

Contributor:

O'Regan, Donal.

Series:

Universitext

Language:

English

Subjects (All):

Differential equations.

Physical Description:

xii, 321 pages : illustrations ; 24 cm.

Place of Publication:

New York ; London : Springer, 2008.

Summary:

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 material, each with an "answers or hints" section, Covers an array of advanced topics which allow for flexibility in developing the subject 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.

Contents:

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

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.

Notes:

Includes bibliographical references (pages [315]-317) and index.

ISBN:

0387712755

9780387712758

0387712763

9780387712765

OCLC:

181090518