Remember that scene in Star Wars Episode IV where Luke is trying to blow up the Death Star, and turns off his targeting computer because a voice in his head told him to rely on the Force instead? And even though it sounds crazy and everyone at mission control was rightly pissed off that he was needlessly gambling their future on his schizophrenia working to their advantage, it all worked out in the end?
Yeah, you're gonna want to follow Luke's lead.
The bulk of this course is very visual, dealing with planes and lines and distances and intersections and surfaces and so on. You'll also be given a broad range of tools to apply to the mathematical constructs defining these objects, from basic 3D applications of Pythagoras' theorem (interesting fact - Pythagoras actually ran a religious cult) to Lagrange multipliers (interesting fact - the analysis behind these was said to be so elegant it resembled a poem) to finding approximations because the original problem was just too damn hard to solve (interesting fact - I am not currently wearing pants).
As a result, it's important to develop intuition on the course content and visualise what each question is asking for, so that you may best choose which tool to use. Take a moment to switch off your mental targeting computer and get a feel for the problem at hand. You're no longer a math student sitting in a tough exam; you're a blonde wizard with an awesome sword, a psychotic father and a sister with cinnamon buns for hair, being guided through life by a dead hermit and a tiny green collection of wrinkles and meaningless advice.
God, I love Star Wars.
The ODE content is a little like Luke's training in the swamp with Yoda (kinda neat, but not too interesting), while the intro vector calculus part is a little like Obi-Wan's seemingly straightforward but actually dickishly cryptic and misleading statement that Vader killed Luke's father that won't really be explained until the sequel (you'll understand it all in MATH2000). Make sure you get the ODE stuff down pat. Understanding the vector calculus part is probably heavily reliant on getting a good lecturer - hopefully one with better grammar than that halfwit Yoda who can't even string a sentence together properly but nevertheless gives Luke advice on saving the universe.
Overall, the course isn't any harder than I was on seeing Leia in that metal bikini, which is to say you'll probably want to 'rewind' the material once or twice for a better look but it won't drive you crazy. Just like A New Hope is structured much like The Phantom Menace but infinitely more enjoyable to watch, I found MATH1052 to be similar but far superior to MATH1051.
I'm still not wearing pants.
Semester 2 - 2013
Lots of visual learning
Lecturer was sometimes hilariously awkward
No Jar Jar Binks
Lost my graphics calculator in one of the lectures
Final fifth of the course contains seemingly random content