MU02035 Mathematical Methods in Physics and Engineering I

Mathematical Institute in Opava
Winter 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Oldřich Stolín, Ph.D. (lecturer)
RNDr. Jiří Jahn, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course covers parts of the demands for the final examination for the specialization Applied Mathematics the program Mathematics.
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
    recommended literature
  • W. J. Hilbert. Modern Algebra with Applications. New York, 2004. ISBN 0-471-41451-4. info
  • J. Munkres. Topology. Prentice Hall, New Jersey, 1999. ISBN 0-131-81629-2. info
  • Kvasnica J. Matematický aparát fyziky. Academia, Praha, 1989. info
  • D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989. info
  • Segethová, J. Základy numerické matematiky. Karolinum, 1988. info
  • N. J. Bloch. Abstract Algebra with Applications. Englewood Clifs, 1987. ISBN 0130009857. info
  • VITÁSEK, E. Numerické metody. SNTL, Praha, 1987. info
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
  • S. MacLane, G. Birkhoff. Algebra. Bratislava, 1974. info
  • A. G. Kuroš. Kapitoly z obecné algebry. Academia Praha, 1968. info
  • K. Rektorys a spolupracovníci. Přehled užité matematiky. SNTL, Praha, 1968. 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.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (recent)
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