Implicit Curves: Analysis & Regular Points

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Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

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

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

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.

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

Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.