F3082 Review of Mathematics

Faculty of Science
Autumn 2015
Extent and Intensity
0/2. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Tue 14:00–15:50 F3,03015
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The aim of the course is the repetition and practical training in mathemtaics needed for theoretical physics, study, especially algebra of vector spaces, linear mappings and tensor spaces, as well as integration of functions and differential forms. Students obtain:
* deeper understanding of mathematical tools for theoretical physics;
* good review concerning the connection of mathematical tools to problems in physic;
* calculation practice.
Syllabus
  • 1. Vector spaces of a finite dimension, scalar product.;
  • 2. Linear mappings of vector spaces, dual spaces.;
  • 3. Linear operators in vector spaces, eigenvalues and eigenvectors.;
  • 4. Tensor spaces, covariant tensors.;
  • 5. Infinitedimensional vector spaces, Hilbert space.;
  • 6. Linear operators in Hilbert spaces, eigenvalue problem and physics.;
  • 7. Riemann integral in n-dimensional Euclidean spaces, transformation of integral.;
  • 8. Diferential forma and differential forms calculus (exterior derivative, pullback).;
  • 9. Integral of differential forms, general Stokes theorem.;
  • 10. Apllications: practical integral calculus.;
  • 11. Differential forms and their integration in phdysics, integral and differential physical laws: mechanics, continuum mechanics, electrodynamics, thermodynamics, quantum mechanics, relativity theory.;
  • 12. Integral of differential forms in variational problems.;P> 13. Calculus.;
  • 14. Calculus.
Literature
    recommended literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně). 697 pp. ISBN 978-80-214-4071-5. 2012. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno. 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. 2009. info
  • SPIVAK, Michael. Calculus on manifolds :a modern approach to classical theorems of advanced calculus. 27th print. Cambridge, Massachusetts: Perseus books. xii, 146 s. ISBN 0-8053-9021-9. 1998. info
  • MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství. 281 s. 1989. info
  • KRUPKA, Demeter and Jana MUSILOVÁ. Integrální počet na euklidových prostorech a diferencovatelných varietách. Vyd. 1. Praha: Státní pedagogické nakladatelství. 320 s. 1982. info
  • MOTL, Luboš and Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Karolinum. 348 s. ISBN 8024604213. 2002. info
Teaching methods
Class discussions, homewoks and their presentations.
Assessment methods
2 written tests, 1 conclusion test
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2013, Autumn 2014, autumn 2017.
  • Enrolment Statistics (Autumn 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2015/F3082