Calculus – Vector calculus

We study the calculus of vector fields, functions that assign vectors to points in its domain. See for instance these examples from daily life. In particular we define line integrals, which can be used to find the work done by a force field in moving an object along a curve. We also define surface integrals, which can be used to find the rate of fluid flow across a surface. The connections between these new types of integrals and the usual single, double and triple integrals are given by higher-dimensional versions of the fundamental theorem: Green's theorem, Stokes' theorem and Gauss's divergence theorem.

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Last modified on October 7, 2021