An Introduction to Ordinary Differential Equations

2. Introduction

3. Historical Notes

4. Exact Equations

5. Elementary First-Order Equations

6. First-Order Linear Equations

7. Second-Order Linera Equations

8. Preliminaries to Existence and Uniqueness of Solutions

9. Picard's Method of Successive Approximations

10. Existence Theorems

11. Uniqueness Theorems

12. Differential Inequalities

13. Continuous Dependence on Initial Conditions

14. Preliminary Results from Algebra and Analysis

15. Preliminary Results from Algebra and Analysis (Contd.)

16. Existence and Uniqueness of Solutions of Systems

17. Existence and Uniqueness of Solutions of Systems (Contd.)

18. General Properties of Linear Systems

19. Fundamental Matrix Solution

20. Systems with Constant Coefficients

21. Periodic Linear Systems

22. Asymptotic Behavior of Solutions of Linear Systems

23. Asymptotic Behavior of Solutions of Linear Systems (Contd.)

24. Preliminaries to Stability of Solutions

25. Stability of Quasi-Linear Systems

26. Two-Dimensional Autonomous Systems

27. Two-Dimensional Autonomous Systems (Contd.)

28. Limit Cycles and Periodic Solutions

29. Lyapunov's Direct Method for Autonomous Systems

30. Lyapunov's Direct Method for Nonautonomous Systems

31. Higher-Order Exact and Adjoint Equations

32. Oscillatory Equations

33. Linear Boundary Value Problems

34. Green's Functions

35. Degenerate Linear Boundary Value Problems

36. Maximum Principles

37. Sturm—Liouville Problems

38. Sturm–Liouville Problems (Contd.)

39. Eigenfunction Expansions

40. Eigenfunction Expansions (Contd.)

41. Nonlinear Boundary Value Problems

42. Nonlinear Boundary Value Problems (Contd.)

43. Topics for Further Studies

Keywords: MATHEMATICS / General MAT000000