Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | doc. Ing. Dalibor Lukáš, Ph.D. | Subject version guarantor | doc. Ing. Dalibor Lukáš, Ph.D. |

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 3 | Semester | winter |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Bachelor |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Combined | Credit and Examination | 10+10 |

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.

Lectures

Tutorials

Project work

In this course numerical methods for selected problems of mathematical analysis are tought. We shall also prove convergence rates and present efficient implementation.

- O. Steinbach, Numerische Mathematik 1. TU Graz, 2005.
- A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics. Springer, 2007.

- W.H. Press, B.P. Flannery, S.A. Teukolski, W.T. Vetterling, Numerical Recipes in C. Cambridge University Press, 1990.

Průběžná kontrola studia:
2 průběžné písemné testy, každý za 0 - 10 bodů.
Podmínky udělení zápočtu:
Pro udělení zápočtu je zapotřebí 15 bodů.

Successful defense of semestral project of point value 0 - 20.

Subject code | Abbreviation | Title | Requirement |
---|---|---|---|

470-2102 | MA 1 | Mathematical Analysis I | Recommended |

470-2103 | MA2 | Mathematical Analysis II | Recommended |

470-2105 | MAIT | Mathematical Analysis for IT | Recommended |

470-2106 | MA2PM | Mathematical Analysis II | Recommended |

470-2201 | LA1 | Linear Algebra | Recommended |

470-2202 | LA-IT | Linear Algebra | Recommended |

470-2203 | LAM | Linear Algebra with Matlab | Recommended |

Subject has no co-requisities.

Lectures:
Errors in numerical computations
Solution of non-linear equations: fixed point theorem, Newton method
Iterative solution of systems of linear equations
Eigenvalues and eigenvectors
Interpolation: polynomial, trigonometric, spline
Approximation:least square method, Tchebyshev metod
Numerical differentiation and quadrature
Numerical solution of initial value problem for ordinary differential equations
Projects:
The aim of the projects is solution of practical problem using numerical methods and their comparison with exact solution.
Project solution:
Problem analysis and proposal of appropriate numerical solution
Numerical solution
Exact solution and comparison with numerical solution
Discussion and conlusions
Excercises:
Introduction to Matlab
Error estimation on examples, computing of computer epsilon
Roots separation of nonlinear equations. Solution of nonlinear equations using bisection method, fixed point iterations and Newton method. Conditions of convergence. Solutions of systems of non-linear equations.
Jacobi and Gauss-Seidel nad SOR methods for solution of systems of linear equations.
Solution of systems of linear equations using steepest descent method and conjugate gradient method. Preconditioning.
Methods for finding of characteristic polynomial. Power method for largest and smallest eigenvalues.
Similarity transformations, Jacobi method, Givens, Housholder and Lanczos methods.
Lagrange and Newton interpolating polynomial, piecewise linear and cubic spline functions.
Least square method and normal equations. Systems of orthogonal functions.
Numerical differentiations.
Numerical quadrature: Newton-Cotes and Gauss formulae.
Numerical solution of initial value problem for ordinary differntial equations: Euler method, Runge-Kutta method.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 40 | 15 |

Examination | Examination | 60 | 11 |

Show history

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2019/2020 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2018/2019 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2018/2019 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2017/2018 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2017/2018 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2016/2017 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2016/2017 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2015/2016 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | P | English | Ostrava | 3 | Choice-compulsory | study plan | |||

2015/2016 | (B2647) Information and Communication Technology | (1103R031) Computational Mathematics | K | English | Ostrava | 3 | Choice-compulsory | study plan |

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