Exam I will be held in the usual room at the usual time: 11:30-12:20 on Monday Sep. 23. It will start promptly at 11:30, so make sure you're on time. The test will cover sections 1.1, 1.2, 1.4, 1.5, 1.6, 3.1, 3.2, and 3.3.

The test will have four problems, possibly with several parts each. Calculators or other devices are not needed and are not to be used.

The following topics are likely to be covered, though the exam is not limited to these topics:

• the notions of general solutions, and particuar solutions satisfying initial conditions
• separable equations, checking for singular solutions
• first order linear equtions; using an integrating factor
• substitution, to get a new (hopefully better) equation; knowing various types of substitutions that are likely to help (eg. Bernoulli, homogeneous, inspired guesses)
• exact equations
• reducible second order equations, using substitution (missing x, missing y)
• higher order linear equations: homogeneous and non-homogeneous; the form of the general solution in both cases
• complementary and particular solutions in the non-homogeneous case
• homogeneous constant coefficient equations: the characteristic equation and using roots to find general solutions
• linear independence and the Wronskian

Advice: I recommend practicing many problems of each type, much more than the number I assigned for homework. For each type of problem you should try to reach the point where you have completely mastered it, and will be happy when you one on the exam. The only way to reach this point is by extensive practice. Remember, if you're uncomfortable now about a certain kind of problem, it may be even more difficult under the pressure of an exam situation.

When it comes time for the test itself, relax and do the best you can. Because you have studied, you know which topics you know best, and can get those problems out of the way quickly. Then you'll have plenty of time to spend on the remaining ones.