Smoothness

Related lectures (29)

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

Covers the approximation of functions in Sobolev spaces using smooth functions.

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

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

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

Covers the Quadratic Sieve method for integer factorization, emphasizing the importance of choosing the right parameters for efficient factorization.

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

Explores non-analytic smooth functions, their properties, and applications in differential geometry and partitioning unity.

Discusses advanced optimization techniques, focusing on faster and projected gradient descent methods in machine learning.

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