Difference between revisions of "Surface integral"

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A '''surface integral''' is the summation of the values taken by a function, typically a [[vector]], over every point in the region of a surface.  Its most common use is to express the flux of a vector field ''F'' (such as a electric force) over a particular surface ''S'':
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A '''surface integral''' is the summation of the values taken by a function, typically a [[vector]], over every point in the region of a surface.  If the surface integral is of a vector function, then it typically entails a [[dot product]] of the vector function with the vector normal (perpendicular) to the surface.
  
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The most common use of a surface integral is to express the flux of a vector field ''F'' (such as an electric force) over a particular surface ''S''.
  
A '''surface integral''' is typically solved by projecting the surface onto a coordinate plane, and then performing a double integral over the coordinates for that plane.
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There are three common techniques for solving surface integrals:
  
[[Category:vector analysis]]
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*projecting the surface onto a coordinate plane, and then performing a double integral over the coordinates for that plane.
[[Category:calculus]]
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*applying [[Stokes' Theorem]]
[[Category:mathematics]]
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*applying the [[Divergence Theorem]]
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[[Category:Vector Analysis]]
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[[Category:Calculus]]
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[[Category:Mathematics]]

Latest revision as of 20:48, September 1, 2016

A surface integral is the summation of the values taken by a function, typically a vector, over every point in the region of a surface. If the surface integral is of a vector function, then it typically entails a dot product of the vector function with the vector normal (perpendicular) to the surface.

The most common use of a surface integral is to express the flux of a vector field F (such as an electric force) over a particular surface S.

There are three common techniques for solving surface integrals:

  • projecting the surface onto a coordinate plane, and then performing a double integral over the coordinates for that plane.
  • applying Stokes' Theorem
  • applying the Divergence Theorem