In mathematics, a surface integral is a definite integral taken over a surface (which may be a curve set in space); it can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over its scalar fields (that is, functions which return numbers as values), and vector fields (that is, functions which return vectors as values).

Surface integrals have applications in physics, particularly with the classical theory of electromagnetism. The definition of surface integral relies on splitting the surface into small surface elements:

<<image /static/files/Math/800px-Surface_integral_illustration.png width:400>>

An illustration of a single surface element. These elements are made infinitesimally small, by the limiting process, so as to approximate the surface:
<<image /static/files/Math/429px-Surface_integral.png width:400>>
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Sat, 20 Aug 2011 11:06:24 GMT
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