Parametric Curves: Descartes' Folium

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Parametric Curves: Analysis and Applications

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

Vector Calculus: Line Integrals

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

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Regular Curves and Constant Speed

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

Regular Curves: Parametrization and Tangent Vectors

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

Asymptotes in Parametric Curves

Explores asymptotes in parametric curves, symmetries, tangent vectors, and qualitative studies near stationary points.

Parametric Curves: Infinite Branches

Discusses parametric curves with infinite branches and the behavior of functions near asymptotes.

Geometrical Aspects of Differential Operators

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

Curves with Poritsky Property and Liouville Nets

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

Curves in Space: Parametric Equations and Surfaces

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