Final Exam Review Math 412-200 (Summer II, 2011)
General Information
The Final Exam (Wednesday, August 10, 10:30-12:30) will be
comprehensive. It will have 6 to 8 questions, some with multiple
parts. The problems will be similar to homework problems, examples
done in class and examples worked out in the text. I will have extra
office hours on Monday, from 1-2, and on Tuesday, from 9:30-1
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Calculators. You may use scientific calculators to do numerical
calculations logs, exponentials, and so on. You
may not use any calculator that has the capability of doing
algebra or calculus, or of storing course material.
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Other devices. You may not use cell phones, computers, or any
other device capable of storing, sending, or receiving information.
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Coverage. The material covered includes everything prior to
Test 2 and sections 7.7, 7.8.4, 10.1-10.3, 10.4.2, 10.4.3. Material
after Test 2 will account for 30-35% of the test.
Topics Covered after Test 2
- Problems in two space dimensions
- Be able to separate variables in the wave equation and heat
equation, in a region with any shape, to arrive at an eigenvalue
problem involving a Helmholtz equation. (Notes, 8/1/11. Also, see
§7.2)
- Be able to separate variables in the Helmholtz equation in polar
coordinates. (§§7.7.1, 7.7.2)
- Be able to obtain eigenfunctions and eigenvalues in
vibrations in a circular drumhead, including the relationship to
Bessel functions. Know the orthogonality relations for Bessel
functions. (§§7.7.3, 7.7.4)
- Be able to solve Bessel's equation via series. (§§7.8.4
and notes for 8/3/11)
- Fourier Transforms
- Know how to find the Fourier transform or inverse Fourier
transform of simple functions. (§§10.1-10.3, 10.4.2, and
10.4.3. You will be given the list of properties on p. 468.)
- Be able to use Fourier transform techniques to solve problems
similar to obtaining the heat kernel. (§§10.4.2, 10.4.3)
- Be able to prove the convolution theorem. (§10.4.3 and Notes
for 8/5/11)
Updated: August 5, 2011 (fjn)