I'm done with your term ¡­

I'm done with your term papers (I still accept more of them!). They are very briefly annotated, but you should all read the following general remarks and see for yourselves whether they apply to you.

• Some of you give references to the text book. That is of course fine, but if you know the result then you need not spend those minutes finding the proper reference. It is not required on the math exams. It is however an idea to spend a word when applying a known result, e.g. ¡°by the extreme value theorem¡±.

Re 2003 problem 2:

• You fared well on this.
• Notice that part (c) tells you to verify a particular solution. Having done that, you can solve (b) by solving the corresponding homogeneous.

Re 2003 problem 3:

• Only a couple of you mentioned the constraint qualification. Fair enough. If you need that on an exam, we'll be precise about it in the problem text.

Re 2004 problem 2:

• (a): some of you really need to refresh differentiation, and not to mention the properties of the parabola p(p+1).
• (a) and (b): As long as we are on a set with noenmpty interior, it suffices that the Hessian is nonnegative and f''xx and f''yy are both nonpositive. That yields the conclusions.
• (c): Sufficiency follows from concavity. Most of you got that right.
• (d): Here's where many of you lose the logic. Too few of you pointed out when you had found the stationary point, that it actually solves. Worse is, many of you concluded with 'only possible point' without making any claim whatsoever that a solution does exist (it follows from sufficiency under part (c) ¨C simple as that). (Do you need to find all solutions? Logically you should, and in this case it isn't hard either, but I announced in class that if that is an issue, then we'll be clear about it in the problem text.)
• I suspect that some of you really didn't get the logic, but answered sufficiently well nevertheless more or less by coincidence; on an exam that has to be good enough, but please have a look at what you wrote and why ¨C it is better to know than to rely on luck.

Re 6-15:

• Generally well solved.
• Part (b) was an ¡°explain how¡± formulation. Many of you did indeed solve, which is way beyond the call of duty, but I guess you would rather err on the side of caution. The main point of this question was that you need the cosine in A sin 3t + B cos 3t. (If you point out ¡°we'll usually need the cos too¡±, the exam committee will understand that you have gotten it just right.)

¨C Nils