Differentiability and Composition

Related lectures (26)

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Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Explains differentiability in LR functions and introduces the Jacobian matrix.

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

Covers differentiability theorems and methods to check for differentiability in functions.