MU02034 Mathematical Methods in Physics and Engineering I

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Oldřich Stolín, Ph.D. (lecturer)
RNDr. Oldřich Stolín, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA ( BN )
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
Course objectives
The student can theoretically describe and practically use basic methods of solving common and partial differential equations.
Syllabus
  • 1. Runge-Kutta method for solving the Cauchy problem for ordinary differential equations.
    2. Mesh method for boundary value problems.
    3. Contractive operators, Banach fixed point theorem, direct iterative method.
    4. Functionals in Hilbert space, minimum of quadratic functional, variational formulation of booundary value problem.
    5. Ritz method, finite elements.
    6. Polynomial approximation, least square method.
    7. Spline interpolation.
Literature
    required literature
  • Burden R. L., Faires J. D. Numerical analysis. Boston, USA, 2011. ISBN 978-0-538-73351-9. info
    recommended literature
  • Segethová, J. Základy numerické matematiky. Karolinum, 1988. info
  • E. Vitásek. Numerické metody. SNTL, Praha, 1987. info
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
    not specified
  • Rektorys K. a spolupacovníci. Přehled užité matematiky II. Prometheus, 2003. ISBN 80-7196-181-7. info
  • Rektorys K. a spolupacovníci. Přehled užité matematiky I. Prometheus, 2000. ISBN 80-7196-180-9. info
  • Škrášek J., Tichý Z. Základy aplikované matematiky III. SNTL, Praha, 1990. ISBN 80-03-00111-0. info
  • Kvasnica J. Matematický aparát fyziky. Academia, Praha, 1989. info
  • Škrášek J., Tichý Z. Základy aplikované matematiky II. SNTL, Praha, 1986. info
  • Dettman, J. W. Matematické metody ve fyzice a technice. Academia, Praha, 1970. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
The all demands for credits are determined by consideration of the tutorial lecturer.
Pass the exam (written and oral).
ActivityDifficulty [h]
Cvičení20
Domácí příprava na výuku84
Přednáška20
Příprava na zápočet16
Příprava na zkoušku16
Summary156
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2020/MU02034