Surface Integrals of Vector Calculus
Date: 01/05/99 at 16:29:46 From: David McLaren Subject: Vector Calculus - Divergence Theorem I am struggling generally with the question below. I have tried taking divF and integrating over the surface, but I think that I am going way wrong with the integration. Find the SURFACE_INT(F dS) of the vector field F = (x^3, y^3, z^3) through the surface of the solid circular cylinder of radius r and length L, given parametrically by m(a,b,c) = (a cos(b), a sin(b), c) 0 <= a <= r, 0 <= b <= 2pi, 0 <= c <= L, using the divergence theorem. Help!
Date: 01/05/99 at 19:17:38 From: Doctor Schwa Subject: Re: Vector Calculus - Divergence Theorem The divergence theorem says: The surface integral of F dS on the boundary of a region is equal to the volume integral of the divergence of F on the inside. So the divergence theorem turns your problem into finding the divergence of F, then doing a triple integral of that (cylindrical coordinates are probably easiest ...) That is, you were right to take div F, but you're supposed to integrate it over the VOLUME, not the surface. If you need more of a hint, please write back! - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/
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