Curves and Surfaces

Related lectures (29)

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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Explains the parametric equations of surfaces of revolution generated by curves in space.

Covers regular curves and constant speed, with examples of circles and helices.

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Covers the concept of parametrized curves in 2D and their properties.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Covers the concept of line integrals and their application in vector fields.