Differential Geometry as a Tool of Natural Sciences
No description for this lecture
Feb. 23, 2021
noon - 2 p.m.
Affine space; How to describe a vector in curvilinear coordinates
March 2, 2021
noon - 2 p.m.
Vectors, covectors and transport operators; Tangential beam. Vector field commutator
March 9, 2021
noon - 2 p.m.
Transport operators in coordinates. A vector tangent to the curve; Dynamic systems. One-parameter, local transformation group
March 16, 2021
noon - 2 p.m.
Lie derivative. Vector field commutator
March 23, 2021
noon - 2 p.m.
Commutativity of single-parameter groups and the commutator of vector fields; Distributions, foliations, formations Frobenius on integrability
March 30, 2021
noon - 2 p.m.
Integrable distributions. Curve orientation. Vector field integration; Force field potential. Differential forms and their external product.
April 6, 2021
noon - 2 p.m.
Operations on differential forms; Integration of differential forms. External differential.
April 13, 2021
noon - 2 p.m.
Lie derivative of the differential form. Sundries with border; Stokes' theorem
April 20, 2021
noon - 2 p.m.
Once again, theorem Stokes. Closed forms and complete forms; Poincare's lemma. Cohomologies. Dual representation of the differential form.
April 27, 2021
noon - 2 p.m.
Once again, dual representation. Riemann geometry; Metric tensor. Isomorphism between vectors and covectors. Scalar product of differential forms.
May 4, 2021
noon - 2 p.m.
Form of volume. Surface area: oriented, non-oriented, zero; Curve length. Dualism ("Star") by Hodge
May 11, 2021
noon - 2 p.m.
Once again about Hodge's duality ("star"). Laplace-Beltrami operator; A simple formula for the Laplacian in arbitrary curvilinear coordinates
May 18, 2021
noon - 2 p.m.
Vector analysis; Continuity equation. Tensors. Spherical functions.
May 25, 2021
noon - 2 p.m.
Local reference frames. Gravitational field; Curvature theory. Covariant derivative of tensor fields. Metric connection
Declaration of Accessibility
Software development:
Andrzej Sawicki
Polish National Agency for Academic Exchange
The Project is financed by the Polish National Agency for Academic Exchange under the Foreign Promotion Programme