Parametric Curves: Envelope and Caustics

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Explores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.

Surfaces in Space

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

Curves in Space: Parametric Equations and Surfaces

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

Surface of Revolution

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

Differential Geometry: Parametric Curves & Surfaces

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

Curves with Poritsky Property and Liouville Nets

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

Interpolation and Calculus

Covers revisions on calculus, derivation rules, interpolation, and tangent vectors.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Implicit Function Theorem: Tangent Hyperplane

Explores the implicit function theorem for n=2 and n=3, focusing on tangent hyperplanes.

Curvature and Osculating Circle

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