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Lecturer(s)
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Janda Martin, Ing. Ph.D.
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Šmídl Václav, Prof. Ing. Ph.D.
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Mach František, Doc. Ing. Ph.D.
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Přikryl Jan, Dr. Ing.
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Ševčík Jakub, Ing.
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Noháč Karel, Doc. Ing. Ph.D.
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Krýsl Pavel, Ing.
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Kadlec Martin, Ing.
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Course content
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1. Introduction to numerical mathematics 2. Linear dynamic systems, ordinary differential equations 3. Numerical methods of solving ordinary differential equations 4. Systems of linear equations 5. Introduction to partial differential equations 6. Numerical methods of solving partial differential equations 7. Interpolation, approximation, search for roots of non-linear equations 8. Normal distribution, examples of Gaussian distribution 9. Fundamentals of regression analysis, least squares method 10. Applied probability and statistics, general regression, selection of regressions 11. Downsampling, bootstrap, cross validation 12. Single and multicriterial optimisation, convex optimisation 13. (reserved, or continuation of optimisation)
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Learning activities and teaching methods
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- Individual project (40)
- 12 hours per semester
- Team project (50/number of students)
- 12 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
- Contact hours
- 52 hours per semester
- unspecified
- 36 hours per semester
- Contact hours
- 16 hours per semester
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| prerequisite |
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| Knowledge |
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| explain fundamental principles of linear algebra (e.g. vector, linear space and its basis, solving systems of linear equations, eigenvalues) |
| explain fundamental terms of calculus (derivative, integral, shape of a graph, rate of change, norm) |
| determine derivatives and integrals of fundamental functions |
| Skills |
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| use the Matlab system as a calculator for matrices and vectors |
| write a simple task in the Matlab programming language |
| calculate the solution of a system of linear equations |
| calculate simple derivatives and integrates of composite functions |
| Competences |
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| N/A |
| N/A |
| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| explain fundamentals of mathematical modelling of dynamic phenomena |
| describe possible sources of errors in numerical computing |
| describe methods of approximate numerical solutions to ordinary differential equations |
| compile a suitable rule for numerical solution of ordinary or partial differential equations |
| explain the principle of optimization and basic optimization methods |
| Skills |
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| compose a cost function for given optimalisation problem |
| apply library methods for solving ordinary differential equations |
| perform an iterative calculation of the solution of the partial differential equation by the method of finite differences |
| evaluate the quality of regression for given data using cross validation |
| recognize the weak regression dependence for given data |
| evaluate the quality of a regression model for given input data |
| use regression analysis knowledge to gradually improve linear regression models |
| Competences |
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| N/A |
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Self-study of literature |
| One-to-One tutorial |
| Skills |
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| Practicum |
| E-learning |
| Individual study |
| One-to-One tutorial |
| Competences |
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| E-learning |
| Practicum |
| assessment methods |
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| Knowledge |
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| Written exam |
| Skills |
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| Skills demonstration during practicum |
| Seminar work |
| Project |
| Projekt je skupinový |
| Competences |
|---|
| Seminar work |
| Skills demonstration during practicum |
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Recommended literature
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Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. An introduction to statistical learning: with applications in R. 2017. ISBN 978-1-4614-7137-0.
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Heath, Michael T. Scientific computing : an introductory survey. 2nd ed. Boston : McGraw-Hill, 2002. ISBN 0-07-239910-4.
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