Math 315 Midterm Exam 1 Review Material
Friday September 22, 2006 10:10-11AM in Todd 420
This will be a closed book Exam. No calculators allowed.

Coverage: Sections 1.1-1.3; 2.1-2.8; 3.1-3.

1. Terminology - Understand what terms mean and how to use:
   differential equation, order, initial value(s), direction field, linear, nonlinear, exact, integrating factor, integral curve, separable, autonomous, exponential growth, logistic growth, stable or unstable equilibrium, homogeneous, nonhomogeneous, characteristic equation, Wronskian, superposition principle, fundamental set, linearly (in)dependent.

2. Techniques - Be able to use with simple problems:
   • solution of 1$^{st}$ order linear equations using integrating factors;
   • solution of first order equations using separation of variables;
   • solution of exact first order equations;
   • use of initial value(s) to determine final solution;
   • determination and classification of equilibrium solutions;
   • solution of second order constant coefficient homogeneous linear equations;
   • approximate solve of 1$^{st}$ order equations using Euler's method;
   • computation of Wronskians.

3. "Facts" and Theorems - Be able to use this information:
   • existence and uniqueness theorem(s) for solutions to first order equations;
   • existence and uniqueness theorem for solutions to second order equations;
   • Abel's Theorem.