Mathematical Modelling

Type of study	Follow-up MasterMaster
Language of instruction	English
Code	310-3340/02
Abbreviation	MM
Course title	Mathematical Modelling
Credits	4
Coordinating department	Department of Mathematics and Descriptive Geometry
Course coordinator	Mgr. Ivona Tomečková, Ph.D.

Subject syllabus

Principles of mathematical modeling. Model quantities.
Basic relations, local and global balance.
One-dimensional stationary states.
Classification of boundary problems. Corectness of mathematical model.
Non-stationary processes - one-dimensional case. Initial problems.
Method of characteristics for the PDEs of the first order.
Application - free thermal convection.
PDEs of the second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDEs.
Multi-dimensional stationary states.
Fourier method for elliptic PDEs. Boundary problems for multivariate problems.
Facultative themes.

Literature

[1]
William E.: Partial Differential Equation Analysis in Biomedical Engineering - Case Studies with MATLAB, 2013

[2]
Kulakowski, Bohdan T.; Gardner, John F.; Shearer, J. Lowen: Dynamic Modeling and Control of Engineering Systems, 3rd Edition, 2007

[3]
Mathematical Modelling: Classroom Notes in Applied Mathematics (Ed. M.S. Klamkin). SIAM Philadelphia, 3rd printing, 1995.

Advised literature

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994

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