Smoothness

Related lectures (29)

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

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.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

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

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

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Covers remarks and demonstrations on function continuity and differentiability, focusing on class C functions.

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