MU:MU03256 General Relativity I - Course Information
MU03256 Mathematical Foundations of the General Theory of Relativity I
Mathematical Institute in OpavaWinter 2010
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: z (credit).
- Teacher(s)
- doc. RNDr. Michal Marvan, CSc. (lecturer)
doc. RNDr. Michal Marvan, CSc. (seminar tutor) - Guaranteed by
- doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Geometry (programme MU, M1101)
- Geometry (programme MU, N1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematical Analysis (programme MU, N1101)
- Theoretical Physics (programme FPF, M1701 Fyz)
- Theoretical Physics (programme FPF, N1701 Fyz)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Secondary School Teacher Training in Mathematics (programme FPF, M7504)
- Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)
- Course objectives
- Mathematical tools and methods of use in General Theory of Relativity.
- Syllabus
- Differentiable manifolds, smooth mappings, algebra of smooth functions.
Tensor fields, tensor product, symmetries.
Afinne connection, geodesics.
Covariant derivative of tensor fields, torsion and curvature.
Riemannian a pseudo-Riemannian structures, Levi-Civita connection.
Lie derivative of tensor fields, Killing field.
- Differentiable manifolds, smooth mappings, algebra of smooth functions.
- Literature
- recommended literature
- M. Kriele. Spacetime: Foundations of General Relativity and Differential Geometry. 1999. ISBN 978-3540663775. info
- L. Krump, V. Souček, J. A. Tůšínský. Matematická analýza na varietách. Praha, Karolinum, 1998. info
- O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995. info
- S. W. Hawking, G. F. R. Ellis. The large scale structure of space-time. Cambridge University Press, 1973. info
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Teacher's information
- Oral examination.
- Enrolment Statistics (Winter 2010, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2010/MU03256