Pushforward (differential)

Related lectures (14)

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

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

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

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

Delves into tangent vectors as equivalence classes on manifolds, highlighting their abstract nature and role in optimization.

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

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

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

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.

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

Covers the analysis of parametric curves and their tangent vectors, focusing on applications and geometric interpretations.

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Explores the Local Inversion Theorem and extremum points in functions.

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