Smooth sets and functions: Charts and atlases

Related lectures (31)

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Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

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

Explores the definition of connections for smooth vector fields on manifolds.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Covers smooth sets and functions on manifolds, with a focus on constructing an atlas for a circle.

Explores smooth functions on manifolds, emphasizing continuity and atlas topologies.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.