Part IA, Vector Calculus
"In the downstairs plane..."
"As soon as you hear the word 'symmetric matrix', you go into autopilot."
"You derive this [the equation for motion in a circle] by being circular..."
"We have a family of curves ruling the surface."
"The usual get-out for not having to define what I mean."
"This can make sense, but in this course we don't particularly want it to."
"Then we could simply do these nine integrals." (evidently for a strange definition of 'simply'...)
"There's a better way of remembering it, which I've forgotten."
"I'm sure you'll have seen this in Dr Stewart's [Dynamics] course - those of you who are going to it..."
"The w's dropped off - I'll probably find it in some other example."
"We can prove this - in fact, we have proved it."
"That's a fairly heavy square brackets here."
"If you're not the outward bound type, I understand it [a saddle point] can be called a pringle point, named after those pieces of cardboard you can buy in a cardboard tube." (He said this last year as well, and his fan club presented him with a tube in the last lecture.)
"The curvature is called the curvature because it's the curvature"
"There is just one joke in these 24 lectures"
"Let's hear it for "
"Also called Gauss's theorem, which doesn't distinguish it from most other theorems in pure maths" (on the divergence theorem)
"I'm going to do this in a way that's sort of true - I don't want to have to wave my arms about and talk about small things"
"Let's think of it concretely as a fluid"
"And you do the delta delta thing and mess around with the indices" (The hokey-cokey in suffix notation?)