Stokes' theorem, also known as the Kelvin-Stokes theorem, is a fundamental theorem in vector calculus that relates a line integral around a closed loop to a surface integral over the surface enclosed by the loop.
Green's theorem, a fundamental concept in vector calculus, relates a line integral around a closed curve (C) to a double integral over the plane region (D) enclosed by the curve. It essentially connects the circulation around a closed loop to the "sum" of infinitesimal rotations within the enclosed area.
Stokes' theorem is an extremely powerful result in mathematical physics. It allows us to quantify how much a vector field is circulating or rotating, based on the integral of the curl.
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0:00 Stoke's Theorem Overview
6:59 Green's Theorem
12:22 Geometric Explanation
16:30 Examples
18:45 Green's Theorem to Compute Land Areas
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