Non-analytic Smooth Functions

Related lectures (32)

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

Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

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

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

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Covers optimization on manifolds, smoothness, tools needed for optimization, and advanced algorithms using Hessians and Riemannian connections.

Explores smooth functions, n-dimensional charts, compatibility, and atlases for manifolds.

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.