Curves: differentiability and smoothness

Related lectures (29)

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Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Explores the increment theorem and derivatives in calculus, focusing on polygonal valleys and curve traces.

Covers continuity, differentiability, and applications in calculus with an emphasis on fundamental concepts.

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

Explains partial derivatives, Hessienne matrix, and their properties.

Explores differentiable functions in R², including vector fields and coordinate transformations.

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Explores the length of continuously differentiable paths using integrals and parametrizations.

Explores differentiability, tangent planes, and algebraic derivatives in functions of two variables.