Non-analytic Smooth Functions

Related lectures (32)

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

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

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

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

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

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

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

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

Explores gradient descent methods for optimizing functions on manifolds, emphasizing small gradient guarantees and global convergence.