These last two examples (and Stokes' theorem in general) are are the subject of vector calculus. They play important roles in [[electrodynamics]]. The divergence and curl operations are cornerstones of [[Maxwell's Equations]].
These last two examples (and Stokes' theorem in general) are are the subject of vector calculus. They play important roles in [[electrodynamics]]. The divergence and curl operations are cornerstones of [[Maxwell's Equations]].
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Stokes' Theorem is a lower-dimension version of the Divergence Theorem, and a higher-dimension version of [[Green's Theorem]]. Green’s Theorem relates a line integral to a double integral over a region, while Stokes' Theorem relates a surface integral of the curl of a function to its line integral.
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Stokes' Theorem is a lower-dimension version of the Divergence Theorem, and a higher-dimension version of [[Green's Theorem]]. Green’s Theorem relates a line integral to a double integral over a region, while Stokes' Theorem relates a surface integral of the curl of a function to its line integral. Stokes' Theorem originated in 1850.