
Dec. 03. Office hours for the rest of the semester:
Time:  WF 15:00 – 16:20  Location: 457 CAB 
Instructor:  Xinwei Yu  xinwei.yu@gmail.com 
Office hours: WF 13:00 – 14:30  527 CAB, 4925731 
Grading & Homework Policy:
Lecture Notes:
Introduction.  
01  Introduction  (Sep. 03)  02  The CauchyKowalevski Theorem  (Sep. 08) 
03  Distributions  (Sep. 10)  
Elliptic Equations  
04  Laplace/Poisson equations – Explicit formulas  (Sep. 17)  05  Hölder Estimates for the Poisson Equation  (Sep. 19) 
06  Harmonic Functions  (Sep. 24)  07  The Perron Method  (Sep. 26) 
08  The Dirichlet Principle  (Oct. 01)  09  Regularity Theory for Weak Solutions  (Oct. 03) 
10  General Linear Elliptic Equations  (Oct. 08)  11  Viscosity solutions  (Oct. 10) 
Parabolic Equations  
12  Heat Equation: Explicit Formulas  (Oct. 17)  13  Maximum Principles  (Oct. 22) 
14  Energy Method  (Oct. 29)  15  Semigroups  (Oct. 31) 
16  Brownian Motion  (Nov. 05)  
Wave Equations  
17  Wave Equations: Explicit Formulas  (Nov. 07)  18  Uniqueness and Asymptotics  (Nov. 12) 
Conservation Laws  
19  Discontinuous Solutions  (Nov. 14)  20  The Single Conservation Law  (Nov. 19) 
21  The Single Conservation Law (cont.)  (Nov. 21)  22  The Riemann Problem  (Nov. 26) 
23  TBA  (Nov. 28)  24  TBA  (Dec. 03) 