Closed Surfaces and Integrals

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Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

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

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

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

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

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

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

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