Lecture

Curves in Space: Parametric Equations and Surfaces

Related lectures (31)

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

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.

Curves with Poritsky Property and Liouville Nets

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

Surface Integrals: Regular Parametrization

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

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Curves and Surfaces

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

Surface Integrals: Implicit Surfaces

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

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Curves: Parameterized Curves and Tangent Vectors

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

Closed Surfaces and Integrals

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

Geometric Areas: Integrals and Regions

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Geometrical Aspects of Differential Operators

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

Geodesics on Surfaces

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

Surfaces in R^3: Curves and Regular Surfaces

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

Intrinsic Geometry of Regular Surfaces

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