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Lecturer(s)
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Brandejský Tomáš, doc. Ing. Dr.
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Course content
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Students within the study of this subject will separatelly solve a few of selected problems from studiied subject. The main topics of the course: *Mathematical logics, theory of sets and theory of Measure. *Advanced matric calculus. Tensor calculus. Generalized inverse. *Differential equations. Numeric methods of differential equations solving. *Large systems of linear differential equations. Chosef sets of nonlinear differential equations. *Integral equations. *Partial differential equations and their systems. *Calculus of variations with applications. Finite element method. *Complex variable functions. Fourier transform. *Matematical optimization. Linear programming. Quadratic programming. *Non-linear regression, splines.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Methods of individual activities
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Learning outcomes
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Within the frame of this subject, the knowledge of mahtematical analysis, linear algebra, theory of functions of a complex variable, Ordinary differential equations, partial differential equations, differential geometry, numerical mathematics will be increased
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral examination, Written examination, Home assignment evaluation
The student completes at least 3 consultations during the semester concerning the theoretical content of the course. The student will pass at least 1 consultations concerning the assigned mathematical problem. Independent solving of requied mathematical problems.
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Recommended literature
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Buckley, J.J. Fuzzy Statistic. 2004.
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Černý, Ilja. Analýza v komplexním oboru. Praha: Academia, 1983.
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Dahlquist, G., Bjőrck, A. Numerical Methods. 2003.
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Drábek, P. Integrální rovnice. 1991.
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Horová Ivana a Jiří Zelinka. Numerické metody, 2. rozš. vydání. Brno: Masarykova univerzita, 2011. ISBN 80-210-3317-7.
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Nocedal, J., Wright, S. J. Numerical optimization. Springer Verlag, 1999.
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PLESNÍK, J. a kol. Lineárne programovanie.. Bratislava: ALFA, 1990.
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Ráb, M. Metody řešení obyčejných diferenciálních rovnic. 1998.
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Rao, C.R., Mitra, S.K. Generalized Inverse of Matrices and Its Applications. 1971.
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Rao, S.S. Engineering optimization. Theory and Practice.. 1996.
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Strichartz, R.S. A Guide to Distribution Theory and Fourier Transforms. 1994.
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Turkington, D.A. Generalized Vectorization, Cross-Products, and Matrix Calculus. 2013.
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