Lectures related to Geometrical Aspects of Differential Operators

Covers the concept of parametrized curves in 2D and their properties.

Covers regular curves and constant speed, with examples of circles and helices.

Explores potential derivatives, Green theorem, simple curves, and adherence in open domains.

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

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Discusses kinematic quantities and linear mass density in examples of metal wires.

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

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

Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.