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Http://mathematicsgu Ru.files.wordpress.c Om/2013/04/89.pdf

89.pdf
Preview of http://mathematicsgu ru.files.wordpress.c om/2013/04/89.pdf
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📊 Size: 344 KB
📄 Pages: 56 pages
⬇️ Downloads: 70

Summary

It defines Euclidean n-space, tangent vectors, and vector fields, and explains how these concepts are used in differential geometry. The main points include:

Definition of Euclidean n-space as the set of ordered n-tuples
 Introduction of tangent vectors as ordered pairs (X, p), where X is an ordinary vector and p is the position vector of the foot of the arrow
Definition of the tangent space at a point p, denoted by Tp(Rn), as the collection of all tangent vectors at that point
 Explanation of vector fields as smooth functions from an open subset U of Rn to the tangent bundle T(U)
Discussion of the directional derivative of a function f at a point p in the direction of a tangent vector Xp
 Introduction of the concept of linear derivations on the space of smooth functions, which are identified with vector fields.

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Description

It defines Euclidean n-space, tangent vectors, and vector fields, and explains how these concepts are used in differential geometry.

Technical Information

  • File Format: PDF
  • File Size: 344 KB
  • Pages: 56
  • Language: EN
  • Total Downloads: 70
  • Last Updated: 2 months ago

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