surface integral

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.

Word History and Origins

Origin of surface integral¹

First recorded in 1870–75

Example Sentences

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.

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Then the quantity E cos θdS is the product of the normal component of the force and an element of the surface, and if this is summed up all over the surface we have the total electric flux or induction through the surface, or the surface integral of the normal force mathematically expressed by ∫E cos θdS, provided that the dielectric constant of the medium is unity.

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