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An Introduction to Ordinary Differential Equations
Overview of attention for book
An Introduction to Ordinary Differential Equations
Springer New York
Table of Contents
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Book Overview
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Chapter 1
Introduction
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Chapter 2
Historical Notes
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Chapter 3
Exact Equations
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Chapter 4
Elementary First-Order Equations
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Chapter 5
First-Order Linear Equations
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Chapter 6
Second-Order Linera Equations
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Chapter 7
Preliminaries to Existence and Uniqueness of Solutions
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Chapter 8
Picard's Method of Successive Approximations
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Chapter 9
Existence Theorems
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Chapter 10
Uniqueness Theorems
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Chapter 11
Differential Inequalities
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Chapter 12
Continuous Dependence on Initial Conditions
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Chapter 13
Preliminary Results from Algebra and Analysis
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Chapter 14
Preliminary Results from Algebra and Analysis (Contd.)
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Chapter 15
Existence and Uniqueness of Solutions of Systems
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Chapter 16
Existence and Uniqueness of Solutions of Systems (Contd.)
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Chapter 17
General Properties of Linear Systems
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Chapter 18
Fundamental Matrix Solution
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Chapter 19
Systems with Constant Coefficients
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Chapter 20
Periodic Linear Systems
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Chapter 21
Asymptotic Behavior of Solutions of Linear Systems
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Chapter 22
Asymptotic Behavior of Solutions of Linear Systems (Contd.)
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Chapter 23
Preliminaries to Stability of Solutions
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Chapter 24
Stability of Quasi-Linear Systems
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Chapter 25
Two-Dimensional Autonomous Systems
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Chapter 26
Two-Dimensional Autonomous Systems (Contd.)
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Chapter 27
Limit Cycles and Periodic Solutions
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Chapter 28
Lyapunov's Direct Method for Autonomous Systems
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Chapter 29
Lyapunov's Direct Method for Nonautonomous Systems
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Chapter 30
Higher-Order Exact and Adjoint Equations
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Chapter 31
Oscillatory Equations
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Chapter 32
Linear Boundary Value Problems
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Chapter 33
Green's Functions
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Chapter 34
Degenerate Linear Boundary Value Problems
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Chapter 35
Maximum Principles
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Chapter 36
Sturm—Liouville Problems
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Chapter 37
Sturm–Liouville Problems (Contd.)
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Chapter 38
Eigenfunction Expansions
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Chapter 39
Eigenfunction Expansions (Contd.)
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Chapter 40
Nonlinear Boundary Value Problems
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Chapter 41
Nonlinear Boundary Value Problems (Contd.)
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Chapter 42
Topics for Further Studies
Overall attention for this book and its chapters
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Book overview
1. Introduction
2. Historical Notes
3. Exact Equations
4. Elementary First-Order Equations
5. First-Order Linear Equations
6. Second-Order Linera Equations
7. Preliminaries to Existence and Uniqueness of Solutions
8. Picard's Method of Successive Approximations
9. Existence Theorems
10. Uniqueness Theorems
11. Differential Inequalities
12. Continuous Dependence on Initial Conditions
13. Preliminary Results from Algebra and Analysis
14. Preliminary Results from Algebra and Analysis (Contd.)
15. Existence and Uniqueness of Solutions of Systems
16. Existence and Uniqueness of Solutions of Systems (Contd.)
17. General Properties of Linear Systems
18. Fundamental Matrix Solution
19. Systems with Constant Coefficients
20. Periodic Linear Systems
21. Asymptotic Behavior of Solutions of Linear Systems
22. Asymptotic Behavior of Solutions of Linear Systems (Contd.)
23. Preliminaries to Stability of Solutions
24. Stability of Quasi-Linear Systems
25. Two-Dimensional Autonomous Systems
26. Two-Dimensional Autonomous Systems (Contd.)
27. Limit Cycles and Periodic Solutions
28. Lyapunov's Direct Method for Autonomous Systems
29. Lyapunov's Direct Method for Nonautonomous Systems
30. Higher-Order Exact and Adjoint Equations
31. Oscillatory Equations
32. Linear Boundary Value Problems
33. Green's Functions
34. Degenerate Linear Boundary Value Problems
35. Maximum Principles
36. Sturm—Liouville Problems
37. Sturm–Liouville Problems (Contd.)
38. Eigenfunction Expansions
39. Eigenfunction Expansions (Contd.)
40. Nonlinear Boundary Value Problems
41. Nonlinear Boundary Value Problems (Contd.)
42. Topics for Further Studies
Summary
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University of Surrey
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