On the last two days of the block, you will give an in-class presentation on a topic related to PDEs.  You can work individually or in pairs.  Individual presentations should be about 35 minutes long, and pair presentation should be about 50 minutes.  Be sure to leave some time for questions.

Here is a list of possible topics.  The number indicates the size of the group that can work on each topic; pair topics are somewhat more challenging or broad than individual topics:

Proof of Fourier Series Convergence Theorem (2.8)           2
Sturm-Liouville Theory and Buckling Beams (6.4-6.5)      1
The Sampling Theorem (10.1 - 10.2)                                  1
Discrete and Fast Fourier Transform (10.3 - 10.4)              2
Quantum Mechanics (11.1 - 11.2)                                       2
Heisenberg's Uncertainty Principle (11.3)                           1
Turing Instability and Pattern Formation                             2
Insect Swarming                                                                  2
Chemotaxis                                                                          2
Tumor Growth                                                                     2
The Eikonal Equation (Optics)                                             1
Navier-Stokes Equations (Fluid Dynamics)                         2
The Black-Scholes Model (Finance)                                    2
Wavelets                                                                               2
Microscopic Derivation of Diffusion Equation                     1


The numbers in parentheses refer to sections in our textbook that cover these topics.  The other topics are not in our textbook, but resources on them are readily available.  I should also point out that there is a one million dollar prize on offer for solving the Navier-Stokes equations.

If there is some other topic related to PDEs that you would like to present, please let me know.