Tensor calculus.
Differentiable manifolds, tangent bundles.
Maps of manifolds, diffeomorphism.
Lie derivative.
Exterior calculus.
Riemann and pseudo-Riemann geometry.
Covariant derivative, parallel transfer, geodesics.
Torsion and curvature, space of connections.
Metric derivatives, Levi-Civita derivative.
Relation of Lie, exterior, and covariant derivatives.
Submanifolds, integrability, Frobenius theorem.
Integration on manifolds, integrable densities, integral theorems.
The lectures are aimed at students interested in theoretical physics at the end of their bachelor's or the beginning of their master's study.
This course is followed by the course NTMF060 – Geometrical Methods of Theoretical Physics II.
Information about lectures in fall 2021:
Lectures and practicals were scheduled each Wednesday at 14:00–17:10 in lecture room T2.
Both lectures and practicals were taught in person.
Lectures were recorded. Recordings of lectures are available on this page.
The lectures were given in English.
Exam:
Times scheduled for the exams are listed in SIS.
The exam has an oral form. The student gets two theoretical questions and one problem analogous to those solved on practicals. She/he has sufficient time to prepare the answers.
The preferred form of the exam is in person. But in necessary cases, it is possible to take the exam online. Please, contact the lecturer a day before the exam in such a case.
It will be possible to schedule the exam after the winter term. Please contact the lecturer.
Assignment for credit:
To obtain the credit, students need to submit a solution to the assignment:
Starting with the third week, the lectures are accompanied by 60-90 minutes practicals. The practicals are not recorded, but problems discussed in the practicals can be found here.
You can also check the "tutorial" section of the course in 2020, where similar problems have been solved. You can find recordings of the tutorials there. However, they are in the Czech only.