Concept

Surface (mathematics)

Related lectures (31)

Surface Integrals: Regular Parametrization

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

Parametric Surfaces

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

Real Surfaces: Defects and Reconstructions

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

Geometry of Surfaces in R²

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

Ruled Surfaces: Generators and Applications

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

Surface of Revolution

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

Gaussian Curvature and Geodesics

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

Surface Normals: Vector Analysis

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

Surface Geometry: Geodesics and Surface Area

Explores geodesics and surface area calculation for rotationally symmetric surfaces.

Regular Surfaces: Painting with Normal Vectors

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

Surface Integrals: Implicit Surfaces

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

Descriptive Geometry: Cones and Cylinders

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

Implicit Surfaces: Regular Points

Explains regular points on implicit surfaces and their relationship with gradients and tangent planes.

Surfaces in R^3: Curves and Regular Surfaces

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

Green's Theorem: Surface Integrals

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

Second Fundamental Tensor

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Closed Surfaces and Integrals

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

Descriptive Geometry: Cones and Cylinders

Covers the definitions and characteristics of cones and cylinders as ruled surfaces with generating lines.

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.