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.

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Presentation transcript:

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 at a Point 8.5 Local Expression for the Differential 8.6 Curves in a Manifold 8.7 Computing the Differential Using Curves 8.8 Rank, Critical and Regular Points Problems

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 at a Point

8.5 Local Expression for the Differential

8.6 Curves in a Manifold

8.7 Computing the Differential Using Curves

8.8 Rank, Critical and Regular Points

Problems

Solution:

Hint:

Solution:

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