### Course: Applied Mathematics

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 Course title Applied Mathematics KAP/AM*D Lecture Doctoral not specified Winter and summer 0 Czech Compulsory-optional Face-to-face Course does not contain work placement None
Lecturer(s)
• Brzezina Miroslav, doc. RNDr. CSc.
Course content
Systems of ordinary differential equations (ODR). Especially linear ones with constant coefficients. Own numbers and matrix vectors. Stability of the solution. Numerical solution of Cauchy tasks for n-th order differential equations and first-order systems in normal form (single- and multi-step methods). Numerical solution of boundary problems for ordinary 2nd order differential equations, shooting method, boundary conditions method, network method. Interpolation and approximation. The smallest square method. Quadrature formulas. Numerical solution of systems of linear equations. Partial Differential Equations (PDR). Marginal and mixed tasks. Network Method. Mathematical basics of the finite element method. Triangulation of the area. Basic finite elements

Learning activities and teaching methods
Lecture
Learning outcomes
Systems of ordinary differential equations (ODR). Especially linear ones with constant coefficients. Own numbers and matrix vectors. Stability of the solution. Numerical solution of Cauchy tasks for n-th order differential equations and first-order systems in normal form (single- and multi-step methods). Numerical solution of boundary problems for ordinary 2nd order differential equations, shooting method, boundary conditions method, network method. Interpolation and approximation. The smallest square method. Quadrature formulas. Numerical solution of systems of linear equations. Partial Differential Equations (PDR). Marginal and mixed tasks. Network Method. Mathematical basics of the finite element method. Triangulation of the area. Basic finite elements

Prerequisites
unspecified

Assessment methods and criteria
Combined examination

Recommended literature
• Braess, D. Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics Cambridge University Press. Cambridge, 2001.
• Brzezina M., Veselý J. Obyčejné (lineární) diferenciální rovnice a jejich systémy. Liberec, 2012. ISBN 978-80-7372-909-7.
• Stoer J., Bulirsch R.:. Introduction to Numerical Analysis. Springer. ISBN 0-387-95452-X.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester