Integrals On Manifolds

Piotr Mikusiński and Michael D. Taylor
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Piotr Mikusiński: University of Central Florida, Department of Mathematics
Michael D. Taylor: University of Central Florida, Department of Mathematics

Chapter 5 in An Introduction to Multivariable Analysis from Vector to Manifold, 2002, pp 153-188 from Springer

Abstract: Abstract In mathematics and its applications one may encounter situations in which it is desirable to set up integrals over arcs or surfaces or their higher dimensional generalizations. (These higher dimensional generalizations are called manifolds. We shall explain them later in this chapter.) For instance, given a mass distributed along an arc with a known density, find the total mass along the arc. Or given a fluid flow through a surface with a given rate of flow at each point of the surface, find the total flow through the surface at any given instant of time.

Keywords: Open Subset; Dimensional Manifold; Variable Formula; Measurable Subset; Inverse Function Theorem (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0073-4_5

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