An Introduction to Ordinary Differential Equations (Paperback, 2008)

Preface.- Introduction.- Historical Notes.- Exact Equations.- Elementary First Order Equations.- First Order Linear Equations.- Second Order Linear Equations.- Preliminaries to Existence and Uniqueness of Solutions.- Picard's Method of Successive Approximations.- Existence Theorems.- Uniqueness Theorems.- Differential Inequalities.- Continuous Dependence on Initial Conditions.- Preliminary Results from Algebra and Analysis.- Preliminary Results from Algebra and Analysis (Contd.).- Existence and Uniqueness of Solutions of Systems.- Existence and Uniqueness of Solutions of Systems (Contd.).- General Properties of Linear Systems.- Fundamental Matrix Solution.- Systems with Constant Coefficients.- Periodic Linear Systems.- Asymptotic Behavior of Solutions of Linear Systems.- Asymptotic Behavior of Solutions of Linear Systems (Contd.).- Preliminaries to Stability of Solutions.- Stability of Quasi-Linear Systems.- Two-Dimensional Autonomous Systems.- Two-Dimensional Autonomous Systems (Contd.).- Limit Cycles and Periodic Solutions.- Lyapunov's Direct Method for Autonomous Systems.- Lyapunov's Direct Method for Non-Autonomous Systems.- Higher Order Exact and Adjoint Equations.- Oscillatory Equations.- Linear Boundary Value Problems.- Green's Functions.- Degenerate Linear Boundary Value Problems.- Maximum Principles.- Sturm-Liouville Problems.- Sturm-Liouville Problems (Contd.).- Eigenfunction Expansions.- Eigenfunction Expansions (Contd.).- Nonlinear Boundary Value Problems.- Nonlinear Boundary Value Problems (Contd.).- Topics for Further Studies.- References.- Index