We ek 
Date  Contents  References 
1  0902 
Imagine UBC Day  
0904  outline, examples of DEs, basic questions, concepts of
solutions Part I. Classical linear equations §2.1 transport equation with constant velocity, Duhamel's principle 
[E,§2.1] 

2  0909  §2.2 Laplace equation and
Poisson equation, fundamental solution, theorem
on solution
formula  [E,§2.2] 
0911  proof of
solution
formula, mean value property, maximal principle 

3  0916  MP for subharmonic function,
uniqueness, comparison, smoothness, derivative estimate, realanalyticity


0918  Liouville
theorem, Harnack inequality, existence of BVP, Green's function 

4  0923  Green's function for balls, Dirichlet principle for BVP 

0925  Perron's method of subsolutions for BVP §2.3 Heat equation fundamental solution and solution formula, maximal principle in bounded domains 
[GT, §2.8] [E, §2.3] 

5  0930 
proof of maximal principle in bounded domains, mean value
property and Hopf's boundary lemma, maximal
principle in whole space

[E, §2.3] 
1002 
uniqueness, Tychonoff example, smoothness and derivative
estimates  [J], [E] 

6  1007 
§2.4 wave equation time
reversibility, energy, D'Alembert's formula, spherical means

[E, §2.4] 
1009 
solution formulas in 2d and 3d, domains of dependence
and influence, nonhomogeneous problem 

7  1014 
Part II. Sobolev
spaces Motivation with elliptic PDE, Banach spaces, Holder spaces, Lebesgue spaces, weak derivative 
[E, Ch.5] 
1016 
Sobolev
spaces, Leibniz rule and as Banach spaces, approximations by smooth
functions 

8  1021 
approximations by smooth
functions II, extension, trace 

1023 
Imbedding inequalities 

9  1028 
Imbedding continued, compactness of imbedding, Poincare inequality.  
1030 
H^{1} Part III. Weak solutions of elliptic equations Weak solutions, LaxMilgram theorem 
[E, Ch6]  
10  1104 
First existence theorem, Fredholm Alternative, second
existence theorem 

1106 
Second and third existence theorems, regularity 

11 
1111 
Remembrance Day  
1113 
Interior, boundary and global H^2 regularity 

12 
1118 
maximal principle, Hopf lemma, strong maximal principle 

1120 
Part IV. Linear evolution
equations weak formulation, Banachspace valued Sobolev spaces, Galerkin method 
[E. Ch.7] 

13 
1125 
Existence and energy bound of weak solutions 

1127 
semigroup approach 