Surface Integrals: Implicit Surfaces

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

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Clarifies the use of Jacobian, normal vectors in surfaces, and arccos(z) constraints.

Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Explores the analogy between curves and surfaces, emphasizing the importance of choosing parameters for normal vectors.

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Explores surfaces with variable curvature, discussing their construction and properties.