Tangent bundle

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Related lectures (30)

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.

Connections: Axiomatic Definition

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.

Parametric Curves: Introduction

Covers parametric curves, including examples, symmetry, tangent vectors, and derivative signs.

Comparing Tangent Vectors: Three Reasons Why

Explores the importance of comparing tangent vectors at different points using algorithms and finite differences.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Tangent Vectors: Definition and Applications

Explores the definition and applications of tangent vectors in determining curve directions on surfaces.

Smooth maps on manifolds and differentials

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Local Frames

Covers the concept of local frames, their construction, and limitations.

Parametric Curves: Descartes' Folium

Covers Descartes' Folium, a parametric curve with specific equations and properties, including domain boundaries and tangent vector analysis.

Tangent vectors without embedding space: Revisiting the embedded case

Explores defining tangent vectors without an embedding space, focusing on creating tangent spaces at every point of a manifold through equivalence classes of curves.

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