What is the relation between “Green’s Theorem” and “Stokes’s Theorem”? Explain about the transformations defined in...

What is the relation between “Green’s Theorem” and “Stokes’s Theorem”?

Explain about the transformations defined in these theorems.

What is the most important application and consequence of “Stokes’s Theorem”?

Explain Independence of path?

Expert Solution

Green's theorem in the plane is a special case of Stokes' theorem

this describes the relationship between a line integral around a simple closed curve, C, in a plane and a double integral over the plane region R bounded by C. It is a special (2 D) case of the Stokes theorem.

and Stokes' Theorem describes relationship between a line integral around a simple closed curve, C, in space, and a surface integral over a piece wise, smooth surface. it is 3D version of greens theorem .

Green's theorem in "curl form" is given by

where

P(x,y) i +Q(xy) j and dr = dx i+ dyj

most important application of stokes theorem is that it relates a surface integral of a the curl of the vector field to a line integral of the vector field around the boundary of the surface.

please like ?

Colby Messinger answered 2 years ago

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Question

What is the relation between “Green’s Theorem” and “Stokes’s Theorem”? Explain about the transformations defined in...

Solutions

Expert Solution

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