Date    Chapter/Topics   or   Page/Problems

T  Jan 7    Introduction          Review the final exam from last semester   (Due Th Jan 16)
Th   9      Hamiltonian-Jacobi Equations      
T   14      Hamiltonian-Jacobi Equations
Th  16      Separation of Variables 4.7.1-2 (Due T Jan 21)
T   21      Fourier Transform
Th  23      Introduction to Linear Elliptic PDE
T   28      (snow)
Th  30      Exam 1 (snow)       2.5.2-6  (Due Th Oct 3) 
T  Feb 4    Physical Interpretation of Linear Elliptic PDE
Th   6      Exam 1 (rescheduled)
T   11      (snow)
Th  13      (snow)
T   18      Outline of existence/uniqueness 
            Exam 1
Th  20      Exam 1 rework due. 
T   25      Lax-Milgram Theorem
Th  27      Exam 2 (postponed)
            First Existence Theorem
T  Mar 4    Sobolev Spaces
            Homework/challenge:  Show that 
                 u(x) = 1-|x|^2 is in H_0^1(B_1(0)\{0}) 
Th   6      Properties of weak differentiation in Sobolev space
T   11      Banach space structure (inequalities; background)
Th  13      Section 5.3 Regularization
T   18      Spring Break
Th  20      Spring Break
T   25      Review; Partition of Unity
	    Student Projects/Presentations:  (1) Section 5.3.2
	                                     (2) Section 5.3.3
	                                     (3) Section 5.4
Th  27      Solution Operator (Poincare' and Sobolev Inequalities)
T  Apr 1    Souhayl (Section 5.3.2)
Th   3      Rellich's compactness theorem
T    8      Goel (Section 5.3.3)
Th  10      Weak maximum principle and Poincare'/Sobolev inequalities
T   15      Theory of compact operators on Hilbert space:
            Fredhold alternative and spectral properties
Th  17      Exam 2 (due)
T   22      Main existence theorem
            Parabolic equations
Th  24      Review (last lecture)

Th May 1    Final Exam 2:50-5:40