Smooth sets and functions: Smooth functions, topology, and manifolds

Related lectures (31)

Page 1 of 4

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

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

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

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

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

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

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

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

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

Covers the concept of orientation and degrees in topology, focusing on assigning orientations to manifolds.