Smooth Manifolds: Diffeomorphisms

Related lectures (28)

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Covers the basics of linear mapping and coordinate systems.

Explains linear independence, basis, and matrix rank with examples and exercises.

Discusses gradients on Riemannian submanifolds and the construction of local frames.

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

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

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

Introduces smooth manifolds, emphasizing the importance of submanifolds of linear spaces.

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

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

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