 
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 243 courses given at UCSB
during 20092010. Reproduction and dissemination with the author's
permission only.
Contents
Chapter 1. Linear Systems 1
1.1. Exponential of a Linear Transformation 1
1.2. Solution of the Initial Value Problem for Linear
Homogeneous Systems 3
1.3. Computation of the Exponential 4
1.4. Asymptotic Behavior of Linear Systems 7
Chapter 2. Existence Theory 11
2.1. The Initial Value Problem 11
2.2. The CauchyPeano Existence Theorem 11
2.3. The Picard Existence Theorem 12
