The Final Exam will be at 8:00 a. m. in the usual classroom on Thursday, May 12, 2011. The format and procedure of the exam will be the same as for the in-class exams. Be sure you follow the instructions of each problem, and give the answers requested, but do not waste time doing things that are not required. I will continue the exam until 10:15 a. m., so you should have plenty of time to finish without rushing. The current draft has 80 points possible.

Do not stay up late Wednesday night trying to study at the last minute. That would have a negative payoff.

The emphasis is on first-order linear systems, the eigenvalue method, and Laplace transform methods. The following topics are very likely to appear, although the exam is not limited to them:

1. Solving first-order linear ODE's using an integrating factor.
2. Linear ODE's and IVP's with constant coefficients.
3. Laplace transforms and inverse transforms, partial fraction decompositions, applications to solving ODE's.
4. First-order linear systems, rewriting a higher-order ODE or system as a first-order system, solutions of a first-order linear system.
5. Matrices and determinants, eigenvalues and eigenvectors, application to solving first-order systems with constant coefficients.

Definitions of important concepts are perfectly reasonable questions, and although you do not need to know them word-for-word, you should be able to write down a coherent and accurate definition of any major concept or term.

The following topics will not be covered: velocity and acceleration problems, slope fields, the Existence and Uniqueness Theorem for first-order IVP's, solving first-order ODE's using separation of variables or substitution methods, word problems with draining tanks and the like, pendulums and mass-spring systems, exact equations, over-, under-, and critical damping, the method of undertermined coefficients (I wanted to include it, but just couldn't squeeze it in with so much other material to cover), variation of parameters, phase-plane portraits, complex eigenvalues.

Please note, however, that some homework was assigned during the final week of classes, and it will be covered on the final exam.

As usual, calculators are not needed, although you may, if you really want to, use a non-graphics simple arithmetic calculator without even trig functions or log and exponential, but no mechanical or electronic device more sophisticated that this (this includes iPods, earpieces, etc.). This list of formulas will be included on the exam. Obviously, the more familiar you are with these formulas, the better you will be able to apply them. A formulas list is no substitute for understanding.

As usual, exams from some of my previous differential equations classes can be found at my course pages page. At that time, however, the course syllabus did not include matrix and eigenvalue methods.