Math 315 Midterm Exam 3 Review Material
Wednesday, November 29, 2006 10:10-11AM in Todd 420
Closed book Exam. No calculators allowed.

Coverage: Sections 5.1-2; 6.1-2, 7.1, 7.4-5.

1. Terminology - Understand and know how to use:
   power series, radius of convergence, singular point, recurrence relation, Laplace transform, system of first order differential equations, homogeneous system, nonhomogeneous system, linear system, general solution, fundamental set, Wronskian, phase plane, phase portrait, direction field.

2. Techniques - Be able to use with simple problems:
   • series solution of n$^{th}$ order initial value problems;
   • Laplace transform solution of n$^{th}$ order initial value problems;
   • conversion of n$^{th}$ order initial value problem to system of $n$ first order differential equations;
   • solution of constant coefficient linear first order homogeneous systems of differential equations;
   • phase portrait or direction field sketch for constant coefficient linear first order homogeneous systems of differential equations with $n=2$.

3. "Facts" and Theorems - Be able to use this info:
   • existence of Laplace transforms;
   • existence and uniqueness theorems for solutions to first order systems of differential equations.