Hi friends, sorry that i have posted so many threads recently regarding complex analysis. i am trying hard to understand as much as possible.(adsbygoogle = window.adsbygoogle || []).push({});

anyway i was wondering if anyone had any good geometric interpretation for the equivalence between a differential being exact and it being path independent. I understand the concepts of exactness and path independence but i have a difficult time relating these two

A differential Pdx + Qdy is exact if Pdx+Qdy=dh for some function h. Where a differential of h is = (∂h/∂x)dx + (∂h/∂y)dy

And a function is path independent on a domain D if given two points A and B, we can integrate the function through any path and get the same value.

I can see the connection between exactness and the fundamental theorem of calculus part I (h is like the antiderivative so we can apply the fundamental theorem) but I guess i have a hard to just equating these two concepts because they seem different. so... if a function isn't exact/path independent then we have to be careful about what curve/path we integrate over. But if path independent we can choose anything. I have a hard time grasping exactly (no pun intended) why that is obvious from the exactness condition.

thanks!

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# Understanding geometrically the equivalence between path independence and exactness

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