The material covered on the exam is the union of both in-class exams, 
lecture notes and  homework.

Fourier series: You should know how to calculate Fourier series, and how to 
extend the interval of definition such as to obtain a FS involving only sines 
or only cosines. You should also understand the connection between smoothness 
of the function and how fast the Fourier coefficients go to 0, and the
overshoot phenomenon. 

Separation of variables. We have had this method in cartesian as well as in 
polar coordinates, for various equations: Laplace equation, Laplace eigenvalue 
equation, heat equation, wave equation (vibrations). You should understand the 
principle of the method. Then you are able to find separation solutions to 
equations that are slightly different from the ones studied in class. 

You need to be able to do the basic calculations for the Laplace, heat, and 
wave equation as have been exemplified by previous exams.

You should understand the basic facts stated about the eigenvalue problem for 
the Laplacian in higher dimensions, and it's relation to the heat equation
and to vibrating membranes

For the higher dimensional wave equation, you should understand the effects 
related to finite propagation speed, in particular which initial data 
influence which parts of the solution. 

You may expect reasonably easy calculational problems and also a few 
theoretical questions that require no calculations. 


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Remember that you may prepare three pages of handwritten notes for use 
during the exam. They will be attached to the exam.
You may also take 3 hours rather than the officially alloted two hours.
This is possible due to the fact that we have the classroom longer
and that nobody in class has a conflicting adjacent exam.