Tangent plane | Wikipedia audio article
Channel: wikipedia tts
Date: 02/06/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Tangent_space


00:00:16 1 Informal description
00:03:25 2 Formal definitions
00:04:14 2.1 Definition as the velocity of curves
00:06:16 2.2 Definition via derivations
00:11:27 2.3 Definition via cotangent spaces
00:18:57 3 Properties
00:22:44 3.1 Tangent vectors as directional derivatives
00:23:42 3.2 Basis of the tangent space at a point
00:24:54 3.3 The derivative of a map
00:28:20 4 See also
00:32:02 5 References
00:37:09 6 External links



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Voice name: en-GB-Wavenet-B


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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.