 
Summary: Ordinary Differential Equations
and
Dynamical Systems
Thomas C. Sideris
Department of Mathematics, University of California,
Santa Barbara, CA 93106
These notes reflect a portion of the Math 243ABC courses given at
UCSB. Reproduction and dissemination with the author's permission
only.
Contents
Chapter 1. Introduction 1
Chapter 2. Linear Systems 5
2.1. Definition of a Linear System 5
2.2. Exponential of a Linear Transformation 5
2.3. Solution of the Initial Value Problem for Linear
Homogeneous Systems 8
2.4. Computation of the Exponential of a Matrix 8
2.5. Asymptotic Behavior of Linear Systems 11
Chapter 3. Existence Theory 17
3.1. The Initial Value Problem 17
