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Lecturer(s)
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Course content
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week 1 The difference between analytical and numerical solution. The error of model, the error of method, rounding error in computation on computers. The distribution of errors during calculation, stability. Systems of linear equations - finite methods. Gauss elimination method. week 2 Method of factorization. Inverse of matrix. Determinants. Iterative methods. week 3 Finding roots of one non-linear equation. Methods using only function values, methods using derivatives. week 4 Finding roots of a system of non-linear equations. Newton-Raphson method. Conversion to optimization problem. week 5 Interpolation, numerical differentiation and integration. Lagrange interpolation polynomial, formulae for derivatives, Newton-Cotes quadrature formulae. week 6 1st test week 7 Richardson's extrapolation, Gauss integration. week 8 Fitting of experimental data. Linear regression. week 9 Fitting of experimental data. Non-linear regression. week 10 Numerical integration of ordinary differential equation. Initial value problem. Runge-Kutta methods. week 11 Numerical integration of ordinary differential equation. Multistep methods. week 12 Boundary values problem. Finite difference method. Introduction to finite element method. week 13 2nd test
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Skills training
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Learning outcomes
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The aim of the course is to introduce basic numerical methods necessary to solve common physicochemical problems and tasks of chemical engineering by means of mathematical modelling.
Students will be able to use methods introduced in this course to solve particular problems of subsequent subjects.
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Prerequisites
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Knowledge of topics covered by courses Mathematics I and Mathematics II.
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Assessment methods and criteria
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Oral examination, Written examination
Assignment - active attendance. Examination - consists of theoretic questions and problems.
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Recommended literature
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Epperson J.F. An Introduction to Numerical Methods and Analysis. John Wiley & Sons, 2002.
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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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Kubíček, M. Numerické algoritmy řešení chemicko-inženýrských úloh. Praha: SNTL, 1983.
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Slavíček E. Výpočetní technika pro chemiky. Praha: SNTL, 1983.
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Vitásek E. Numerické metody. SNTL/ALFA, 1987.
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