Lectures related to Differential algebra

Explores the association of Lie algebras to algebraic groups and homomorphisms.

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Covers the basics of differential operators and derivatives for n-tuples and vector fields.

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

Covers derivability, linear applications, composition of functions, and the gradient vector.

Covers the concept of fundamental solutions in the context of differential operators.

Explores conservative forces, potential energy, and total mechanical energy conservation in various examples.

Explores vector fields, potentials, Fourier analysis, and differential operators in scalar fields.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.