Assignment 2

                        Marking Scheme and TA Comments


1. Most students did well on Problems 1, 3, 4(b), 4(c) and 5.

2. In Problem 2, 
      1 pt for sound assumptions, 
      2 pts for correct expression of entries in matrix, 
      4 pts for correct proof that the resulting matrix is diagonally 
        dominant (but not strictly diagonally dominant); strictly 
        diagonally dominant is only true in first and last rows,
      3 pts for correct use of Gersgorin theorem.

   The most common mistake is they (incorrectly) proved the matrix is
   strictly diagonally dominant and said the 0 is not eigenvalue. I took
   off 3-4 pts for this mistake.

3. In Problem 4(a), students are required to answer three questions: 
   (1) 2 pts for c1 is bounded,
   (2) 2 pts for c2 is bounded ,
   (3) 1 pt for c1 > 0.

   Some students said that c1 > 0 because the differential operator
   is elliptic.  But you could have c1 = 0 even if he differential
   operator is elliptic.  More explanation is needed to show that 
   c1 > 0. In this case, I took off 1 pt.

   Some students accidentally didn't show the c1 is upper bounded, I took 
   off 1 pt.

4. For Bonus question, I divided the 10 pts as: 
       3 pts for P1, 
       3 pts for P2 and 
       4 pts for P3. 
   For each part, if they proved the result by themselves or only 
   referenced the Hungarian paper, I gave them full marks. If some 
   other references were used, half of the marks are given then.