Creative research conducted in a field of applied mathematics and co-operation with experts in other engineering and scientific fields are major focuses of the study that the students should master. They are encouraged in a maximum degree possible to engage in research projects of the Institute of Mathematics at the BUT Faculty of Mechanical Engineering. Computers are available to students as standard equipment.

prof. RNDr. Jan Čermák, CSc.

1. Geometrical structures, operators and their applications in the mechanics.

   The aim is the investigation and description of some geometrical structures related to Weil functors and serching for selected kinds of differential operators, particularly on functions and vector fields on the studied or already described structures. The second aim is searching for applications in the continuum mechanics.

   Tutor: Tomáš Jiří, doc. RNDr., Dr.

2. Mathematical modelling of dynamical systems

   Dynamical systems theory provides a useful tool for description and qualitative investigation of many engineering problems. There is a need of profound problem analysis for a construction of adequate mathematical model. Considering too many details is generally leading to complications in the model investigation whereas a negligence of fundamental factors can depreciate obtained analysis. Therefore it is necessary to compare the model analysis with real data (if it is possible). The work consists in applying mathematical and numerical analysis in engineering problems modelling and proper interpretation of obtained results.

   Tutor: Tomášek Petr, doc. Ing., Ph.D.

3. Modern methods for solving nonlinear variationall differential equations

   Since intial boundary value problems for evolutionary mainly partial differential equations in technology often do not admit classical solution, various generalized formulations of these problems were proposed. The aim of the study will be comparison of these formulations and studying existence and uniqueness of their solutions. Then the theory will be applied to particular problems occuring in technology and alternatively to carry out numerical experiments.

   Tutor: Franců Jan, prof. RNDr., CSc.