Tangent space | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Tangent_space


00:00:18 1 Informal description
00:03:44 2 Formal definitions
00:04:37 2.1 Definition as the velocity of curves
00:06:47 2.2 Definition via derivations
00:12:18 2.3 Definition via cotangent spaces
00:20:16 3 Properties
00:24:15 3.1 Tangent vectors as directional derivatives
00:25:16 3.2 Basis of the tangent space at a point
00:26:31 3.3 The derivative of a map
00:30:12 4 See also
00:34:08 5 References
00:39:31 6 External links



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SUMMARY
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In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.