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
-
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.
-
Other devices. You may not use cell phones, computers, or any
other device capable of storing, sending, or receiving information.
-
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)