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

Just as with line integrals, there are two kinds of surface integrals: a surface integral of a scalar-valued function and a surface integral of a vector field.

From Textbooks • Mar. 30, 2016

Therefore, the definition of a surface integral follows the definition of a line integral quite closely.

From Textbooks • Mar. 30, 2016

Figure 6.72 Calculating a surface integral over surface S.

From Textbooks • Mar. 30, 2016

Similarly, when we define a surface integral of a vector field, we need the notion of an oriented surface.

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 Gray, Andrew