MU:MU02034 Math. Methods in Phys. Eng. I - Course Information

MU02034 Mathematical Methods in Physics and Engineering I

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Hynek Baran, Ph.D. (lecturer)
RNDr. Petr Blaschke, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Petr Blaschke, 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

• Applied Mathematics (programme MU, B1101)
• Applied Mathematics (programme MU, N1101)
• Mathematical Methods and Modelling (programme MU, Bc-M)
• General Mathematics (programme MU, Bc-M)
• Mathematics (programme MU, B1101)

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. and J. D. FAIRES. Numerical analysis. Boston, USA. ISBN 978-0-538-73351-9. 2011. info

recommended literature
• Segethová, J. Základy numerické matematiky. Karolinum, 1988. info
• VITÁSEK, E. Numerické metody. SNTL, Praha, 1987. info
• Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava. ISBN 063-559-87. 1987. info

not specified
• Rektorys K. a spolupacovníci. Přehled užité matematiky II. Prometheus. ISBN 80-7196-181-7. 2003. info
• Rektorys K. a spolupacovníci. Přehled užité matematiky I. Prometheus. ISBN 80-7196-180-9. 2000. info
• Škrášek J., Tichý Z. Základy aplikované matematiky III. SNTL, Praha. ISBN 80-03-00111-0. 1990. 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)

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).

Activity	Difficulty [h]
Cvičení	20
Domácí příprava na výuku	84
Přednáška	20
Příprava na zápočet	16
Příprava na zkoušku	16
Summary	156

• Enrolment Statistics (recent)
  
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