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.