Announcements

• Dec. 11. Solution to homework 4 will be here after I have received all submissions.
• Dec. 03. Attention! Anyone who needs extra time for HW4 should contact me to make arrangement. The definite deadline would be Dec. 12 2:30pm since otherwise I cannot post solutions before the exam.

• Dec. 03. Office hours for the rest of the semester:

  • Dec. 5, Dec. 8, Dec. 10, Dec. 12: 1pm – 2:30pm;
  • Dec. 15: 9:30am – 11am.
• Dec. 02. There is a typo in Exercise 3 of Lecture 22. In equation (75), s should be s^˙. Another typo in Exercise 3 of Lecture 19, in equation (44), 0<x<1 should be 0<x<t.
• Dec. 01. Solution to Homework 3 is here.
• Nov. 26. Homework 4: Exercises in lectures 19 – 22. Due: Dec. 10. before 2pm (Please come to my office to hand it in).
• Nov. 26. Homework 3 now due Fri. Nov. 28.
• Nov. 10. Homework 3: Exercises in lecture notes 12 – 18. Due: Wed. Nov. 26.
• Nov. 04. Solutions to the midterm can be found here.
• Oct. 31. Solutions to Homework 2 will be posted before Sunday morning. Check here after Nov. 2, 8am.
• Oct. 28. Homework 2 is due Oct. 31 in class now!
• Oct. 22. Midterm will be held in class on Monday Nov. 3. It will cover lectures 1 – 11.
• Oct. 14. Solutions to homework 1 is here. Please report any mistakes or typos.
• Oct. 10. Homework 2: Exercises in lecture notes 04 – 11. Due: Oct. 29 in class.
• Sep. 23. Homework 1 now due Oct. 1 in class.
• Sep. 10. Homework 1: Exercises in lecture notes 01 – 03. Due: Sep. 24 in class.
• Sep. 10. Scheduel change! Now the lectures are WF 15:00 – 16:20, 457 CAB. Office hours also change to WF 13:00 – 14:30.

• Course website: http://www.math.ualberta.ca/~xinweiyu/527.1.08f.

• Grading & Homework Policy:

  • Final: 50%;Midterm: 20%;Homework: 30%.
  • Midterm will be held in class during the week Oct. 20 – 24.
  • Exams are closed book/notes, no electronic devices are allowed.
  • There will be 4–5 homeworks.
  • Homeworks will be collected in class. The due date will be posted in “Announcements”.
  • Graded homeworks will be returned in class one week after collection.
  • Each homework problem will be graded as if it carries 10 points, but finally all homeworks put together will worth 30% of the total points.
  • Homework problems with “(optional)” in it do not carry any points.
  • Collaboration is encouraged for homeworks but forbidden for exams.

• Lecture Notes:

  	Introduction.
  01	Introduction	(Sep. 03)	02	The Cauchy-Kowalevski 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)