Lecturer(s)


Brzezina Miroslav, doc. RNDr. CSc.

Course content

 Systems of ordinary differential equations (ODE). Especially linear with constant coefficients. Eigenvalues and eigenvectors of matrices. Stability of the solution.  Numerical solution of Cauchy's problem for nth order ODE and firstorder systems in normal form (single and multistep methods). Numerical solution of boundary value problems for ordinary 2nd order differential equations, shooting method, boundary conditions method, finite difference method.  Interpolation and approximation. The least square method. Quadrature formulas. Numerical solution of systems of linear equations.  Partial Differential Equations (PDE). Boundary and mixed problem. Finite difference method.  Mathematical fundamentals of finite element method. Triangulation of the domain. Basic finite elements.

Learning activities and teaching methods

Selfstudy (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Independent creative and artistic activities, Individual consultation, Seminár

Learning outcomes

Individual study of mathematical methods in the field of natural science  applied mathematics, which are used as a suitable tool in industrial applications and specify how these methods can be used.
The student will acquire detailed knowledge of the subject in the area according to the approval of the Branch Board

Prerequisites

Unspecified

Assessment methods and criteria

Oral exam
oral examination before a committee appointed by the Dean. Written work in the recommended range of 20 pages.

Recommended literature


Braess, D. Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics Cambridge University Press. Cambridge, 2001.

Braun, M. Differential Equations and Their Applications. Springer, 1983. ISBN 0387908064.

Brzezina M., Veselý J. Obyčejné (lineární) diferenciální rovnice a jejich systémy. Liberec, 2012. ISBN 9788073729097.

Stoer J., Bulirsch R.:. Introduction to Numerical Analysis. Springer. ISBN 038795452X.
