Lectures related to Regularity of Curves

Curves in the Oriented Plane

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

Parameterization of Curves

Explores parameterization of curves, emphasizing continuous settings and accurate curve representation through various examples.

Surfaces in Space

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

Advanced Analysis II: Length of Continuously Differentiable Paths

Explores the length of continuously differentiable paths using integrals and parametrizations.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Conforming Configurations in Veneering: Pseudosphere Example

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

Curve of Genus 2: Very Ample Divisors

Explores very ample divisors on curves of genus 2 and their implications.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.