Tangent vector

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Related lectures (30)

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Parametric Curves - Introduction

Introduces parametric curves and discusses tangent vectors and symmetry properties.

Parametric Curves: Introduction

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

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Elliptical Arch Construction

Explores the construction of elliptical arches using a single ellipse arc.

Parametric Curves Study Elements

Covers the study of parametric curves and tangent vectors.

Comparing Tangent Vectors: Three Reasons Why

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

Tangent vectors without embedding space: Equivalence classes

Delves into tangent vectors as equivalence classes on manifolds, highlighting their abstract nature and role in optimization.

Parametric Curves: Descartes' Folium

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

Tangent spaces to submanifolds

Introduces tangent spaces to submanifolds and their properties in optimization on manifolds.

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.