Math 5320 Ordinary Differential Equations

Prerequisite: Math 5308

Textbook: Theory of Ordinary Differential Equations, Krieger Publishing Company, 1984

 

Topics:

Chapter 1. Existence and uniqueness of solutions

Existence of solutions

Uniqueness of solutions

Method of successive approximations

Continuation of solutions

Systems of Equations

nth order Equation

Dependence of solutions on Initial Conditions and Parameters

 

Chapter 3. Linear Differential Equations

Linear homogeneous Systems

Nonhomogeneous Linear Systems

Linear Systems with Constant Coefficients

Linear Systems with Periodic Coefficients

Linear Differential Equations of Order n

 

Chapter 13. Asymptotic Behavior of Nonlinear System

Asymptotic Stability

First Variation = Orbital Stability

Asymptotic Behavior of a System

Conditional Stability

 

Chapter 14. Perturbation of Systems having a Periodic Solution

Nonautonomous System

Autonomous System

 

Chapter 15. Two-Dimensional Real Autonomous Systems

Two-Dimensional Linear Systems

Pertubation of Two-Dimensional Linear Systems

Proper Nodes and Proper Spiral Points

Centers

Improper Nodes

Saddle Points

 

References.

 

Levison, Ordinary Differential Equations.