Geometric Areas: Integrals and Regions

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

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

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

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

Covers circle circumference calculation and parametric curve arc length determination.

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

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

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.

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