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Related lectures (30)

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From embedded to general manifolds: upgrading our foundations

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Connections: Axiomatic Definition

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

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.

Tangent Spaces and Submersions

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

Hands on with Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Parametric Curves: Descartes' Folium

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

Kinematics: Curvilinear Abscissa

Covers curvilinear abscissa in kinematics, discussing positive direction and duration comparison.