Timeline for How should one present curl and divergence in an undergraduate multivariable calculus class?
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| Apr 20, 2012 at 4:28 | comment | added | Daniel McLaury | Soon, I was able to learn what had been a full year's worth of material in a few weeks. Whenever I bring this up in mathematical company, I'll always hear the same thing -- "Yeah, me too. I didn't understand any of that stuff until I learned differential geometry." | |
| Apr 20, 2012 at 4:25 | comment | added | Daniel McLaury | I agree wholeheartedly -- despite having the highest score in my vector calculus course, I had absolutely no idea what any of these things meant. I even ended up failing a physics class after finding myself completely unable to make sense of the divs, grads, and curls. Several years later, while trying to get a feeling for homological algebra, I picked up a book talking about de Rham cohomology since I'd heard that it was a good source of practical examples. By the time I was six or seven pages in, I suddenly understood everything I'd spent years struggling with in completely futility. | |
| Jul 14, 2010 at 0:23 | comment | added | David Corwin | I almost feel like the exterior derivative definition of curl is kind of like a mneumonic - all you remember is that differential forms are anti-commutative, and then you basic just work out the curl formula from that! | |
| Apr 21, 2010 at 12:42 | history | answered | muad | CC BY-SA 2.5 |