Exam Post-mortem | Mathematical Methods 3 | January 2019

A1. (a) A significant number of candidates made the mistake of solving the 
        "X-problem" before the "Y-problem". This led to the issue of having
        to find eigenfunctions that satisfy a nonhomogeneous boundary condition. 

    (b) A number of candidates tried to construct the Fourier expansion of
        the function f(x)=1. Doing this did not gain any extra marks!
     
    (c) Most candidates got full marks for this part.

    (d) A number of candidates made no attempt to answer this. The majority of 
        the candidates who did provide an answer simply wrote down the finite 
        difference equation system associated with a two-point boundary
        problem. (This did not get any marks.)

    (e) The majority of candidates who constructed the correct system were able 
        to solve it correctly.


B2. This question proved to be straightforward with almost all candidates 
    getting at least 7 marks overall. A few candidates constructed the wrong 
    Newton iteration and so got the wrong answer in part (c).


B3. This question proved to be challenging. A significant number of candidates
    incorrectly got the correct answer to 4 digits in part (b). The mistake
    that was made was to "simplify" the ODE system by setting x=1 before
    solving it using rk4. Such candidates typically  got 2 marks out of 7 for
    part (b) because the intermediate stage vectors K2, K3, K4 had only one 
    or two digits of accuracy (because the wrong system was being solved). 


B4. This (routine) bookwork question was done well. A number of candidates made
    the mistake of solving the problem in the notes (with a jump at x=1/2) 
    rather than the problem specified in part (b).


End of Comments.