Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a...
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Transcript of Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a...
![Page 1: Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a Map 8.3 The Chain Rule 8.4 Bases for the Tangent Space.](https://reader033.fdocuments.us/reader033/viewer/2022051214/56649f505503460f94c72a48/html5/thumbnails/1.jpg)
Chapter 8The Tangent Space
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Contents:
8.1 The Tangent Space at a Point8.2 The Differential of a Map8.3 The Chain Rule8.4 Bases for the Tangent Space at a Point8.5 Local Expression for the Differential8.6 Curves in a Manifold8.7 Computing the Differential Using Curves8.8 Rank, Critical and Regular Points Problems
![Page 3: Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a Map 8.3 The Chain Rule 8.4 Bases for the Tangent Space.](https://reader033.fdocuments.us/reader033/viewer/2022051214/56649f505503460f94c72a48/html5/thumbnails/3.jpg)
8.1 The Tangent Space at a Point
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8.2 The Differential of a Map
![Page 8: Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a Map 8.3 The Chain Rule 8.4 Bases for the Tangent Space.](https://reader033.fdocuments.us/reader033/viewer/2022051214/56649f505503460f94c72a48/html5/thumbnails/8.jpg)
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8.3 The Chain Rule
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8.4 Bases for the Tangent Space at a Point
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8.5 Local Expression for the Differential
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8.6 Curves in a Manifold
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8.7 Computing the Differential Using Curves
![Page 26: Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a Map 8.3 The Chain Rule 8.4 Bases for the Tangent Space.](https://reader033.fdocuments.us/reader033/viewer/2022051214/56649f505503460f94c72a48/html5/thumbnails/26.jpg)
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8.8 Rank, Critical and Regular Points
![Page 29: Chapter 8 The Tangent Space. Contents: 8.1 The Tangent Space at a Point 8.2 The Differential of a Map 8.3 The Chain Rule 8.4 Bases for the Tangent Space.](https://reader033.fdocuments.us/reader033/viewer/2022051214/56649f505503460f94c72a48/html5/thumbnails/29.jpg)
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Problems
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Solution:
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Hint:
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Solution: