Learning Lagrangian mechanics was like falling in love all over again with your girlfriend when you discovered exactly how elegant she could be. Easily my favorite part of classical mechanics as an undergrad.
Same here. In highschool, I really struggled with classical mechanics. A lot of things didn't click, because they were taught to us before we were taught calculus, and a lot of what I was seeing in class simply didn't make much sense. I understood the words and I could do the math, but never actually felt like I had a grip on it.
Fast forward to my freshman year and poof! mechanics suddely isn't a mess of because-i-said-so formulae that sort of make some physical sense. It's an elegant, well-thought system that can help you understand the world.
I had a further moment of revelation later on, when I seriously studied philosophy. It doesn't look like much now, but when put into their historical context, the discoveries made by Galilei and Newton are amazing leaps in human thought.
Microeconomics is as bad as physics in that respect -- if the course doesn't assume calculus, they wind up reinventing anyway. It's not worth the trouble to study either subject unless knowledge of calculus is assumed.
