Lecture notes and materials

1. 2008-09-01:  Introduction. Derivation of the heat equation.
   
   
2. 2008-09-02:  Characteristics. Quasilinear equations. Burgers' equation.
   
   
3. 2008-09-03:  Non-linear 1st order equations. Envelopes. Examples.
   
   
4. 2008-09-04:  Problem session, I
   
   
5. 2008-09-05:  Higher order PDE. Canonical form. Examples.
   
   
6. 2008-09-08:  The wave equation, I.
   
   
7. 2008-09-09:  The wave equation, II: reflection method and non-homeogeneous case.
   
   
8. 2008-09-10:  The wave equation, III: Spherical means and higher dimensional representations.
   
   
9. 2008-09-17:  canceled
   
   
10. 2008-09-18:  The Laplace and Poisson equations, I.
    
    
11. 2008-09-19:  The Laplace and Poisson equations, II.
    
    
12. 2008-09-22:  Green's function
    
    
13. 2008-09-23:  Problem session, II
    
    
14. 2008-09-24:  Functional spaces
    
    
15. 2008-09-25:  Sobolev spaces I: Distributions and weak derivatives
    
    
16. 2008-09-30:  Sobolev spaces II: Weak problems. Poincare inequality.
    
    
17. 2008-10-07:  Sobolev spaces III: Sobolev inequalities. Sobolev embedding theorems.
    
    
18. 2008-10-07:  Problem session, III
    
    
19. 2008-10-09:  Maximum principles
    
    
20. Solutions to problem session III (part I)
    
    
    Beta (list of some formulas you can use at exam)