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Lecturer(s)
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Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
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Course content
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- 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 n-th order ODE and first-order systems in normal form (single- and multi-step 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.
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Learning activities and teaching methods
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Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Independent creative and artistic activities, Individual consultation, Seminár
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Learning outcomes
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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
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Prerequisites
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Unspecified
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Assessment methods and criteria
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Oral exam
oral examination before a committee appointed by the Dean. Written work in the recommended range of 20 pages.
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Recommended literature
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Braess, D. Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics Cambridge University Press. Cambridge, 2001.
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Braun, M. Differential Equations and Their Applications. Springer, 1983. ISBN 0-387-90806-4.
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Brzezina M., Veselý J. Obyčejné (lineární) diferenciální rovnice a jejich systémy. Liberec, 2012. ISBN 978-80-7372-909-7.
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Stoer J., Bulirsch R.:. Introduction to Numerical Analysis. Springer. ISBN 0-387-95452-X.
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