#### 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**