Geometrical Aspects of Differential Operators

Related lectures (30)

Page 3 of 3

Covers curvilinear integrals in R^n, focusing on continuous functions and curves.

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

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

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

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.

Explores deriving fields from a potential, curvilinear integrals, and necessary conditions for domains.

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.