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Multiple Integrals; Coordinate Systems

  • Klaus Weltner
  • Sebastian John
  • Wolfgang J. Weber
  • Peter  Schuster
  • Jean  Grosjean
Chapter

Abstract

Let us develop the problem by a simple example. A solid cube, as shown in Fig. 13.1, has a volume V. If the density ρ is constant throughout the entire volume then the mass is given by M = ρV. There are cases, however, in which the density ρ is not constant throughout the volume. The density of the Earth is greater near the center than at the surface. The density of the atmosphere is at a maximum at the surface of the Earth: it decreases exponentially with the altitude.

Keywords

Variable Limit Radius Vector Multiple Integral Elemental Area Mass Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2014

Authors and Affiliations

  • Klaus Weltner
    • 1
  • Sebastian John
    • 4
  • Wolfgang J. Weber
    • 5
  • Peter  Schuster
    • 2
  • Jean  Grosjean
    • 3
  1. 1.Institute for Didactic of PhysicsUniversity of FrankfurtFrankfurtGermany
  2. 2.SulzbachGermany
  3. 3.School of Engineering at the University of BathBathUK
  4. 4.JahnsdorfGermany
  5. 5.Computing CenterUniversity of FrankfurtFrankfurtGermany

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