surface integral

American  

noun

Mathematics.

1. the limit, as the norm of the partition of a given surface into sections of area approaches zero, of the sum of the product of the areas times the value of a given function of three variables at some point on each section.

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Etymology

Origin of surface integral

First recorded in 1870–75

Example Sentences

See Examples For:

surface integral

Since some surfaces are nonorientable, it is not possible to define a vector surface integral on all piecewise smooth surfaces.

From Textbooks ● Mar. 30, 2016

Informally, the surface integral of a scalar-valued function is an analog of a scalar line integral in one higher dimension.

From Textbooks ● Mar. 30, 2016

Evaluate surface integral ∬Sx2 yzdS, where S is the part of plane z = 1 + 2x + 3y that lies above rectangle 0 ≤ x ≤ 3 and 0 ≤ y ≤ 2.

From Textbooks ● Mar. 30, 2016

Then the unit normal vector is k and surface integral ∬ curl F · dS is actually the double integral ∬ curl F · kdA.

From Textbooks ● Mar. 30, 2016

It is now well known as Stokes's theorem connecting a certain surface integral with a line integral, and has many applications both in physics and in geometry.

From Lord Kelvin An account of his scientific life and work by Andrew Gray