MATH 375 - Honours Partial Differential Equations, Fall 2012


FOR THE CLASS NOTES, THE URL LINK WAS ANNOUNCED IN CLASS AND WAS ALSO SENT TO YOU BY EMAIL.
THESE NOTES WILL BE PERIODICALLY UPDATED.
NOTES LAST UPDATE ON Nov 28, 2012.

IF YOU DO NOT GET THESE EMAILS PLEASE LET ME KNOW AND I WILL ADD YOU TO THE CLASS LIST.


THE MIDTERM WILL BE IN CLASS ON OCTOBER 19. IT WILL COVER UP TO AND INCLUDING SECTION 6.3.3.
It will be 40% on characteristics
40% on the wave equation
20% on distributions (in particular differentiation and convergence in the sense of distributions)


REVIEW SESSION:
WED. DEC 12, 12 TO 2 PM IN BH1205.
PARTICIPATION IS OPTIONAL. NO NEW MATERIAL WILL BE COVERED AND THERE WILL BE NO NOTES FROM THE SESSION.


FINAL EXAM: You will be allowed TWO 8.5 x 11 double sided sheets of information. Make these sheets carefully.
The exam consists of 10 questions. The first is true or false and will cover the entire course.
Then
1 question on characteristics
1 question on the wave equation
3 questions on the Laplacian, harmonic functions, Green's functions, derivatives in the sense of distributions
1 question on the diffusion equation
1 question on random walks
1 question on Fourier series and eigenfunctions
1 question on separation of variables.


OCT 3 Announcement: You can hand in PS 2 on Tuesday Oct 9. Just leave it in my mail box or under my office door. Also, I have updated the notes --- they include the corrected derivation of the Euler Equations.


Sept 14 Announcement: You can hand in PS 1 on Monday Sept 24. Just leave it in my mail box or under my office door. Also, I have updated the notes and have included a rough version of Chapter 5.


There are two graders for the Homework (I will grade the midterm and final exam).
Spencer Frei spencer.frei@mail.mcgill.ca
Jan Feys feys@math.mcgill.ca


  • Course Outline


  • Problem Set No. 1
    • FOR QUESTION 8, JUST PLOT u(x,1) and u(x,2).

  • Solutions to PS No. 1


  • Problem Set No. 2
    • Typo in Question 4: Last part should say find the general solution of the equation that you derived.
    Typo in Question 6: Initial velocity should be defined as 1 if 3 < x < 4.

  • Solutions to PS No. 2


  • Problem Set No. 3
    • You can hand in on Monday Oct 29.
  • Solutions to PS No. 3


  • Problem Set No. 4 -- You can hand in on Wed Nov 14 (in class)
    • NOTE that I added an 8th question on Oct. 31, 2012.
  • Some Solutions to PS No. 4

    • TYPOs: In 3,4,5, delete the minus sign in front of the Laplacian.

  • Problem Set No. 5
    • NOTE that I added a question on Nov 15, 2012. In question 5, take l = pi.
  • Solutions to PS No. 5