Below are suggested projects for the class. This list might be updated as the course
progresses. If you want more information about any of the proposed projects, contact the
instructor. You can also suggest a different project related to the course content. Contact
the instructor if you wish to work on a project different than the ones suggested below.
You only need to do one project.
Projects can be done in groups of two but students have to submit their assignment
separately on Brightspace (it can be a duplicate copy of the assignment submitted by your
classmate). Make sure to put both your names on the project.
Projects are due on May 5th, 4pm.
Project 1. Use the solutions to the Schro¨dinger equation for the hydrogen atom derived in
class to derive the form of the s, p, d, f orbitals that you learned in chemistry.
Project 2. Derive spherical coordinates in Rn. Use it to find an explicit expression for the
element of integration dS on ∂Br(0).
Project 3. Construct the Green’s function for the Laplacian in the half-space and in a ball
and use it to solve the corresponding Dirichlet problem for Laplace’s equation.
Project 4. Prove Liouville’s theorem for harmonic functions.
Project 5. Prove the Sobolev inequality.