Surface Integrals - Maple Application Center
Application Center Applications Surface Integrals

## Surface Integrals

Author
: Jack Wagner
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In the same way that a vector field may be integrated over a curve, it may be integrated over a surface. To each parallelogram that forms an element of the area of the surface we assign the normal component of the vector field at some interior point. As the partition of the surface is refined the sum of the products of the area of the parallelograms and the normal component of the vector field is the integral of the vector field over the surface, usually written Int(F n, A), where dA is understood to represent the "element of area", and n is the unit normal. This integral is the flux of F through the surface S. Because the normal to the surface plays a key role it is important that we work only with surfaces over which it is possible to consistently define a unit normal. That is, there must be a vector valued function, n(p), that assigns a unique unit normal to each point, p. Such a surface is orientable.

#### Application Details

Publish Date: April 10, 2002
Created In: Maple V
Language: English

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vector-calculus

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