Surface Integrals: Implicit Surfaces

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Surface Integrals: Regular Parametrization

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

Surface of Revolution

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

Closed Surfaces and Integrals

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Curves in Space: Parametric Equations and Surfaces

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

Surface Integrals: Parameterized Surfaces

Explores surface integrals over parameterized orientable surfaces and their applications in flux and work evaluation.

Regular Surfaces: Painting with Normal Vectors

Explores regular surfaces and painting with normal vectors, integral calculations, symmetries, and surface orientation.

Differential Geometry: Parametric Curves & Surfaces

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

Surfaces in Space

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

Green's Theorem: Surface Integrals

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.

Geometrical Aspects of Differential Operators

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