Lecture

Tangent Vectors: Definition and Applications

Related lectures (31)

Differential Geometry: Parametric Curves & Surfaces

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

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Curves and Surfaces

Covers the representation of plane curves and the nature of obtained curves.

Surfaces in R^3: Curves and Regular Surfaces

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

Curves with Poritsky Property and Liouville Nets

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

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Surface of Revolution

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

Ruled Surfaces: Generators and Applications

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

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Closed Surfaces and Integrals

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

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

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

Geometry of Surfaces in R²

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

Intrinsic Geometry of Regular Surfaces

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

Shells I

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

Geometric Surfaces: Paraboloid and Hyperboloid Concepts

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Surface Integrals: Regular Parametrization

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

Surfaces in Space

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

Surfaces with Variable Curvature

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

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Tangent Vectors and Bézier Curves

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.