In simple terms what are differential forms

Differential forms in the ℝn

Vector Analysis pp 11-44 | Cite as

  • Ilka Agricola
  • Thomas Friedrich

Summary

Vectors in Euclidean space \ ({\ mathbb {R} ^ n} \) can be understood as "free vectors" or as "position-bound vectors" at a point of \ ({\ mathbb {R} ^ n} \). In the first case we understand \ ({\ mathbb {R} ^ n} \) simply as a Euclidean vector space. The second approach is based on the idea of ​​\ ({\ mathbb {R} ^ n} \) as a set or a metric space, the elements of which are called the points of space. The position vectors bound to a point form a vector space which, however, changes from point to point. For example, vectors at different points cannot be added. This leads to the concept of tangent space in a point of \ ({\ mathbb {R} ^ n} \).

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Copyright information

© Vieweg + Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2010

Authors and Affiliations

  • Ilka Agricola
  • Thomas Friedrich
  1. 1. Department of Mathematics and Computer Science, Philipps University of Marburg, Marburg
  2. 2nd Institute for Mathematics, Humboldt University, Berlin-Berlin