- parametric curves
- polar curves
- vector-valued functions
- functions of several variables
- partial derivatives
- double integrals
- triple integrals
- polar, cylindrical and spherical coordinates
- planes and tangent planes to surfaces
- directional derivatives and the gradient vector
- Lagrange multipliers
- the Jacobian matrix and determinant
I really loved the course. I'd been nervous but things just clicked this time round -- for example, I remember struggling last year to get the crossproduct of vectors using the 3x3 determinant method and using that long complicated formula instead, but it just clicked seeing this lecturer do it on the board as part of another problem (she didn't revise previous topics). It was the same with integration - I just got the hang of it eventually. One nice thing was that because of that I was good at explaining it to people who hadn't got it yet, because it hadn't come naturally to me. Now I love integration, apart from the long bit at the end with all the arithmetic and errors.
Something I really struggled with during the course was parametrization, e.g. parameterize this curve or this surface. I just didn't understand what it meant or what the point of it was and so I couldn't understand how to use it, but I finally got it just before the exam and it felt brilliant - I was even able to check an answer I got by another method in the exam using parameterization, and that independent verification gave me extra confidence that the answer was right. It was so cool finally cracking it.
The lecturer was brilliant, and it really felt like she set us up for success, which is something that can't be said for all college maths lecturers. She wrote everything out on the board and balanced theory with examples, so there was one example for each concept and she wouldn't go deep into things like the epsilon-delta definition of a limit, she'd just say 'for x arbitrarily close to' so that we could get to the examples. It was so much easier to understand and it was great because I picked up loads of skill with calculus and vectors that I hadn't got before. Yeah there's a place for proofs-based maths, but I really appreciated this course giving us what we needed as scientists.
I wrote down what she was saying and then directly after the lecture or as soon as I had a gap I'd rewrite the notes into another, neater, notebook. She also provided scans of all her notes online in case we missed something.
She gave good homeworks - sometimes challenging but generally just in a fun way, and relevant to the course so there'd usually be some example in the notes we could refer to and see how to approach the problem rather than just searching in the dark. After the deadline, she promptly uploaded the Solutions for that homework so we could check mistakes and learn where we went wrong quickly. Coming up to the exams, she held office hours, and posted (because it was her first year teaching the course) two sample papers and also posted full solutions to them. It was brilliant, as someone with anxiety, to know how I was doing.
Another nice thing she did when I told her that I can't visualise: met with me for an hour outside class to help me come up with ways to 'visualise' the surfaces and solids in other ways so that I could solve the problems.
She also gave a really fair exam - I'd been worried about her giving us random stuff that was just barely mentioned like the triple integral Jacobian or even some stuff that was covered and in homework like symmetry properties of polar curves, but she pretty much just asked us stuff that was central to the course. Or maybe that's just because I'd covered it thoroughly.
My only gripe with the course is that I had some of my homeworks marked down a bunch for things like not putting labels on graphs or not putting coordinates on when it just said to sketch a curve, since I took the word 'sketch' literally. And the TA insulting my graph and calling it a scribble when I complained about it (it wasn't! It was a parabola, it was just very slightly shorter on one end and the center didn't perfectly coincide with the y axis but was close!).
But overall it was a brilliant course and obviously I'm delighted with my score. Helps that I literally couldn't have done better (in the exam). I learned so much that I hadn't even known I didn't know.
(I also liked that I did one maths-for-physics module (this one) and one maths-for-non-physicists module (Stats; it conflicts with one of the Maths modules required for Physics so it's de facto not for physicists), and got 100% in this one, because now I can tell mean physics people to feck off saying I'm bad at maths coz I'm doing biology.)