Second Exam Survival Tips

The exam will cover material from chapters 3, 4, 5, and 7, beginning with 3.3 (might be useful to review 3.1 and 3.2, though) and ending with 7.6. Questions will be divided just about evenly among chapters 3/4, chapter 5, and chapter 7.

Sections not tested include 3.8, 5.5 and 5.6. Chapter 4 will only be covered lightly, since it largely just duplicates chapter 3.

The exam will be about 60% computation (e.g. ``solve the initial value problem ...'') and about 40% comprehension (e.g. ``how do we know that the following gives all solutions of this ODE...'')

A good strategy for practicing computation is to go back through the homework problems and work problems similar to those assigned. The major computational skills you should have acquired are
- solving higher order, constant coefficient, linear, homogeneous ODE's;
- using method of undetermined coefficients;
- finding power series solutions for initial value problems. (remember that there are two ways to go about finding coefficients in the series--recursion and differentiating the ODE);
- determining the radius of convergence of a power series solution to an ODE;
- solving constant coefficient, linear, homogeneous systems.

I like graphical understanding--you can just about count on seeing a direction field, graph of a function, etc somewhere on the exam.

For linear systems with constant coefficients, remember that eigenvectors and eigenvalues of the matrix on the right side are very important.
Major theorems are fair game. You should be able to state things like existence/uniqueness theorems, superposition principal, etc, accurately. You should also have some understanding of what they mean and how they fit in to the ``big picture''.