Description

Qualitative analysis of differential equations

Prerequisites

MATH 410

Topics

The One-Dimensional Problem

Existence
Uniqueness
Continuation of solutions
Separable equations
One-dimensional linear problem
Input/output structure

Linear Systems

Linearity property of solutions
Fundamental matrix solutions
Variation of constants formula
Constant coefficient case
Exponential matrix
Higher order equations
Primary responses
Matrix norms
Linear perturbations

Autonomous Systems

Translation property
Orbits
Phase plane diagrams
Biological models

Stability Theory

Stability notions
Linear characterization of stability
Lyapanov Theory
LaSalle's theorem

The two body problem