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Integrals On Manifolds

In: An Introduction to Multivariable Analysis from Vector to Manifold

Author

Listed:
  • Piotr Mikusiński

    (University of Central Florida, Department of Mathematics)

  • Michael D. Taylor

    (University of Central Florida, Department of Mathematics)

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.

Suggested Citation

  • Piotr Mikusiński & Michael D. Taylor, 2002. "Integrals On Manifolds," Springer Books, in: An Introduction to Multivariable Analysis from Vector to Manifold, chapter 5, pages 153-188, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0073-4_5
    DOI: 10.1007/978-1-4612-0073-4_5
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