Course Unit Code | 470-2501/03 |
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Number of ECTS Credits Allocated | 6 ECTS credits |
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Type of Course Unit * | Optional |
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Level of Course Unit * | First Cycle |
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Year of Study * | Third Year |
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Semester when the Course Unit is delivered | Winter Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 470-2210 | Numerical Linear Algebra 1 |
Name of Lecturer(s) | Personal ID | Name |
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| LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |
Summary |
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In this course numerical methods for selected problems of mathematical analysis are tought. We shall also prove convergence rates and present efficient implementation. |
Learning Outcomes of the Course Unit |
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Numerical methods stands behind computer solutions to complex engineering problems. The course Numerical Methods 1 aims at helping students to choose a proper algorithm for the solution of selected problems of Calculus and analyze the solution regarding stability (sensitivity of the output data on the inputs) and computational complexity. |
Course Contents |
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I. Data fitting: Lagrange interpolation, Chebyshev interpolation, least squares approximation, polynomial regression, orthogonal systems of polynomials (Legendre, Laguerre, Hermite), fast Fourier transform.
II. Numerical integration: Newton-Cotes quadrature, Gauss quadrature (Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite).
III. Iterative methods for solution of nonlinear equations: bisection, fixed-point iterations, Newton method.
IV. Numerical solution to ordinary differential equations: one-step Euler, Crank-Nicholson, and Runge-Kutta methods, multi-step methods, predictor-corrector methods, Galerkin methods, parareal methods.
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Recommended or Required Reading |
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Required Reading: |
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- QUARTERONI, Alfio; SACCO, Riccardo a SALERI, Fausto. Numerical mathematics. 2nd ed. Texts in applied mathematics, 37. Berlin: Springer, c2007. ISBN 978-3-540-34658-6. |
- VONDRÁK, Vít a POSPÍŠIL, Lukáš. Numerické metody 1. Ostrava: VŠB-TU, 2011. http://mi21.vsb.cz
- FEISTAUER, Miloslav a KUČERA, Václav. Základy numerické matematiky. Praha: Matfyzpress, 2014. ISBN 978-80-7378-264-1.
- QUARTERONI, Alfio; SACCO, Riccardo a SALERI, Fausto. Numerical mathematics. 2nd ed. Texts in applied mathematics, 37. Berlin: Springer, c2007. ISBN 978-3-540-34658-6. |
Recommended Reading: |
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- PRESS, William H. Numerical recipes: the art of scientific computing. 3rd ed. Cambridge: Cambridge University Press, 2007. ISBN 978-0-521-88068-8. |
- MÍKA, Stanislav a BRANDNER, Marek. Numerické metody I. Plzeň: Západočeská univerzita, 2000. ISBN 80-7082-619-3.
- DUINTJER TEBBENS, Erik Jurjen. Analýza metod pro maticové výpočty: základní metody. Praha: Matfyzpress, 2012. ISBN 978-80-7378-201-6.
- PRESS, William H. Numerical recipes: the art of scientific computing. 3rd ed. Cambridge: Cambridge University Press, 2007. ISBN 978-0-521-88068-8. |
Planned learning activities and teaching methods |
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Lectures, Tutorials, Project work |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 30 | 15 |
Examination | Examination | 70 | 21 |