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. | + | 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 a 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]] | ||
[[Category:vector analysis]] | [[Category:vector analysis]] | ||
[[Category:calculus]] | [[Category:calculus]] | ||
[[Category:mathematics]] | [[Category:mathematics]] | ||
Revision as of 15:39, January 10, 2010
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 a 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