Description  % of the final grade  Date 
Location and Time 
Remarks 
Midterm  30%  Thu, Feb 27  In class  Review questions. 
Final  35%  Wed, Apr 29 
3pm, location TBA  
HW assignments  35%  on a regular basis (see below)  posted on webpage 
Date  Material covered  Homework  Remarks 
Jan 7  Introduction. Examples of PDEs. 
HW 1. HW 1 Solutions. 
HW 1 due on 1/16 at 5pm. 
Jan 9  The Schrodinger equation and separation of variables. 
Notes on the
Schrodinger equation. 

Jan 14  More on Schrodinger's equation. Separation of variables for the
1d wave equation. 
HW 2. HW 2 Solutions. 
HW 2 is due on 1/23 at 5pm. 
Jan 16  Fourier series. 
Summary of
theorems. 

Jan 21  The 1d wave equation on the real line. D'Alembert's formula. 

Jan 23  More on 1d waves: generalized solutions and propagation of
singularities. Some general tools for the study of PDEs. 
HW 3. HW 3 Solutions. 
HW 3 is due on Jan 30 at 5pm. 
Jan 28  Formal aspects of PDEs: general definitions and notation.
Laplace's and Poisson's equation in R^n. Fundamental solution to
Laplace's equation. 

Jan 30  Existence of solutions to Poisson's equation. Harmonic functions
and their properties. 
HW 4. HW 4 Solutions. 
HW 4 is due on 2/13 at 5pm. 
Feb 4  Project: heat equation. 
Project. Project Solutions. 
Project due on 2/13 at 5pm. 
Feb 6  Project: heat equation. 

Feb 11  More on harmonic functions: maximum principle and selected
results. The wave equation in R^n: finite propagation speed. 

Feb 13  Solutions to the wave equation in R^2 and R^3. 
HW 5. HW 5 Solutions. 
HW 5 is due on 2/20 at 5pm. 
Feb 18  Duhamel's principle. The Minkowski metric, Lorentz fields, and
commutator properties. 
HW 6. HW 6 Solutions. 
HW 6 is due on 2/27 at 5pm. 
Feb 20  Decay of solutions for the wave equation in R^n. 

Feb 25  Review for the test. 

Feb 27  Midterm  
Feb 29  Mar 8  Spring break  
Mar 10  
Mar 12  
Mar 17  
Mar 19  
Mar 24  
Mar 26  
Mar 31  
Apr 2  
Apr 7  
Apr 9  
Apr 14  
Apr 16 