Introduction to Ordinary Differential Equations

ISBN-10: 0387712755
ISBN-13: 9780387712758
Edition: 2008
List price: $59.99 Buy it from $14.78
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Book details

List price: $59.99
Copyright year: 2008
Publisher: Springer
Publication date: 7/29/2008
Binding: Paperback
Pages: 322
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.100
Language: English

Department of Mathematics, National University of Singapore.

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 Nonautonomous 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

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