The final exam for the course will take place in at 9:00am on Tuesday the 9th of December in T-13/125 (next door to the room in which we have lectures).

Please see this Sample exam (solutions) for the format of the exam and a rough indication of scope and difficulty. That a topic appears on the sample is neither an indication that it will nor that it will not appear on the real exam.

(Note: there's an error in the solution to Q1, I got a minus mixed up somewhere. The final answer should be -3/4. Also, in Q2a, the integral should be of t^2, so the answer is 1/3. What's more, on Q3, ||DT|| should be \rho^2 sin\phi, not \rho \sin\phi as written. So the final answer there should be 4\pi / 15. Thanks to Arya for pointing these out. Apologies for any confusion.)

The exam will test the entirety of the course, but will be weighted towards the final third of the course. It will be 3 hours in duration, and will be an open book exam.

The format of the exam will be the same as that of the sample exam. There will be 5 questions, all of which should be answered. One question will test material from the first third of the course, being the part covered by midterm 1; another will test material from the second third, corresponding to midterm 2; the remaining 3 will test the last third of the course.

(This way, each third of the course gets 30% course weight through examinations, the remaining 10% being for the assignments.)

The material covered by the last third of the course:

- Multiple integrals and change of variables;
- Parametrised surfaces and surface integrals;
- Gauss' and Stokes' theorems.

A list of problems from the textbook for revision purposes.