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. 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. | 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 | + | 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: | There are three common techniques for solving surface integrals: | ||
| Line 9: | Line 9: | ||
*applying the [[Divergence Theorem]] | *applying the [[Divergence Theorem]] | ||
| − | [[Category: | + | [[Category:Vector Analysis]] |
| − | [[Category: | + | [[Category:Calculus]] |
| − | [[Category: | + | [[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