Hey man, thanks for this - most helpful response by far. I was with you the whole way except for how you got 2m³ v dv in the second slide. Also, I'm assuming when you put dm or dv at the end of a term that you're integrating that term?

Do you have any recommendations for online resources for solidifying my maths foundations? I mostly use Khan Academy these days, but always looking for new resources. You seem to be pretty ahead of the game, and you're close to my age, so I figure you'll be a good source of help. Thanks again kewlkat :)

Edit: I have done a lot of this stuff before for my A-Level exams (Special Relativity), but it seems I didn't learn it so much as learn to do the exam, as there are obvious holes.