Exam III will be held in the usual room at the usual time: 11:30-12:20 on Monday Nov. 25. It will start promptly at 11:30, so make sure you're on time. The test will cover sections 7.5, 7.6, 8.1, and 9.1 - 9.5.

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:

• Laplace transform of periodic function, shift-and-truncate furmula (translation in t)
• delta functions, relation to step functions, Laplace transform of delta functions
• using step functions to express functions having two cases
• manipulating power series: differentiating, index shifting, substituting into a differential equation
• solving for the coefficients of a power series solution to a differential equation
• recognizing the power series as a familiar function
• computing coefficients of the Fourier series of a periodic function
• even and odd periodic extensions of functions defined on an interval
• the Fourier Sine and Cosine series of a function defined on an interval (obtained by extending as above)
• the heat equation, with two kinds of boundary conditions (constant temperature endpoints, insulated endpoints)
• using the Fourier Sine series of the initial condition u(x,0) = f(x) to write down a solution u(x,t) to the heat equation. Note: you will not be asked to perform separation of variables, or to produce the standard solutions u_n(x,t) on your own; Theorems 1 and 2 of section 9.5 will be provided if they are needed.

We did not cover "Termwise integration of Fourier Series" on p. 605, or "damped forced oscillations" on p. 613.

I will provide a list of Laplace transforms and basic power series for you to use during the exam. Here is the list.

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.