#surface integrals

Moral of the story I have spent this weekend understanding line and surface integrals and integrals over R^3. Green's, Stokes' and Gauss' Theorems. And I I have a good intuitive foundation for these theorems now, and can relate them all to each other. I owe large part of that understand to Khan Academy. Who shares my belief in having intuitive understanding of a topic is 12/10 the most important thing. So it annoys me when I say, I dont understand something. And somewhen else is like 'oh its eassy its just this formula' and then Im like 'okay, explain it to me'. And literally 9/10 they cant. Like that is not understanding it. If you call that understanding then I understand it 12x better than you and I still claim I don't understand. I bet the majority of people in my multivariable and complex calculus have no idea what a line integral actually represents. But in saying all of this intuitively understanding something is nothing if you don't actually know the definition and can answer real questions. Its interesting though cause a postgrad was talking about this the other day and was lke 'you dont have to understand any of it, just know how to use the formulas and answer questions, it will all make sense and you'll understand it next year'. Which is true, you never understand something that well when you're being taught it, but the next year when you use those results it all sorta comes full circle and you get it. But why wait? Try your best to be at that level now and then you cant get fucked over in an exam.