Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Surface (mathematics)

Related lectures (31)

Geometry of Surfaces in R²

Explores the geometry of surfaces in R², including implicit descriptions, critical points, and regular surfaces.

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Green's Theorem: Surface Integrals

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

MHD Equilibrium & Stability

Explores Magnetohydrodynamic equilibrium and stability, ideal MHD solutions, 'hairy ball' theorem, and boundary conditions.

Conforming Configurations in Veneering: Pseudosphere Example

Covers conforming configurations in veneering, focusing on the pseudosphere example.

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Complements of Hypersurfaces in Projective Spaces

Explores the complement problem for hypersurfaces in projective spaces and discusses isomorphism based on their complements.

Surface of Revolution

Covers calculating surface areas of rotated curves using integrals and parameters.

Understanding Jacobian and Normal Vectors in Surfaces

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

Angle Calculation on Regular Surfaces

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.

Surface Integrals: Regular Parametrization Log in to Mediaspace to watch this video

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

Parametric Surfaces Log in to Mediaspace to watch this video

Covers the concept of parametric surfaces and the importance of orientation.

Real Surfaces: Defects and Reconstructions Log in to Mediaspace to watch this video

Explores the difference between ideal and real surfaces, defects, and surface reconstructions.

Ruled Surfaces: Generators and Applications Log in to Mediaspace to watch this video

Explores ruled surfaces, surfaces generated by moving lines in space, including cones, cylinders, and hyperboloids, with applications in architecture.

Surface of Revolution Log in to Mediaspace to watch this video

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

Surface Normals: Vector Analysis Log in to Mediaspace to watch this video

Explains surface normals for parametric and implicit surfaces, focusing on vector analysis and examples with spheres.

Surface Geometry: Geodesics and Surface Area Log in to Mediaspace to watch this video

Explores geodesics and surface area calculation for rotationally symmetric surfaces.

Regular Surfaces: Painting with Normal Vectors Log in to Mediaspace to watch this video

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

Surface Integrals: Implicit Surfaces Log in to Mediaspace to watch this video

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

Descriptive Geometry: Cones and Cylinders Log in to Mediaspace to watch this video

Explains the definitions of cones and cylinders as ruled surfaces and how to find tangent planes to them.