4 ms·
Line / surface / volume integrals are certainly a jump from one-variable integrals.
by beojan 8y ago
Line / surface / volume integrals are certainly a jump from one-variable integrals.
- fooker 8y agoNot a big jump, if you conceptually stick to the 'area under curve' definition. Analytically computing surface/volume integrals, yes, that is a big jump. But I don't understand why students need to memorize N algorithms and M substitution rules for that.
- woopwoop 8y agoWhat is the straightforward "area under the curve" definition of a line integral?
- fooker 8y agoWikipedia has a nice animation for this. https://en.wikipedia.org/wiki/Line_integral#/media/File:Line_integral_of_scalar_field.gif https://en.wikipedia.org/wiki/Line_integral#/media/File:Line...
- woopwoop 8y agoOkay. I am used to this being called a path integral, and the phrase line integral being reserved for the integral of a vector field over a curve. This does not, as far as I know, admit a straightforward definition as an area under a curve.
- fooker 8y agoIf you replace area under curve with volume under surface, it seems to me that the same intuition holds.
- gowld 8y agoSure, and AI isn't a big jump from statistics.
- fooker 8y agoI would say AI:Statistics :: Engineering:Physics . Sometimes it is a big jump, sometimes it is all common sense.