What, physically, are you calculating when you're solving a contour integral?
I was going to post a snarky reply but I stopped when I couldn't actually get an answer. The way I understand it is that contour integration is just one of (infinitely) many ways to compute the closed integral between two points where regular integration only allows one.
>>7715733
I see. How would you visualize it?
fun fact: In german there is no difference between line-, curve-, or contourintegral
basically you're always integrating along a contour in space (real or complex)
I always imagined it like the area under the curve (like a normal integral), only that the base is itself a curve in 2D space, instead of the x axis. I might be wrong, though...
https://en.wikipedia.org/wiki/Line_integral#/media/File:Line_integral_of_scalar_field.gif
this explains it quite well
>>7716201
Love that gif
>>7716201
how would one make such a gif? animate with tikz or something like that?
>>7715714
Scalar conour integral can be seen as area under the contour. Vector contour integral is usually work done by a force field when you move a test particle around the contour.