Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |

Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2019/2020 | Year of cancellation | |

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

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

KUC14 | prof. RNDr. Radek Kučera, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Examination | 3+3 |

Students completing the course will be able to: recognize problems that can be solved numerically; chose a suitable numerical method; decide on the correctness of computed results and on its influence by rounding errors, discretization errors, or errors of another type; identify numerically stable and unstable calculations and characterize them by the condition number; analyze numerical algorithms from the point of view of computational complexities and storage requirements; use the Matlab language and the standard Matlab libraries; propose algorithmically correct implementations of basic numerical methods, write it in the Matlab language, debug and test

Lectures

Individual consultations

Tutorials

Project work

The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis.

[1] QUARTERONI, S., SACCO, R., SALERI, F. Numerical Mathematics. 2. vyd. New York: Springer, 2007. ISBN 978-3-540-49809-4.

[1] SÜLI, E., MAYERS, D., F. An Introduction to Numerical Analysis. Cambridge: University Press, 2003. ISBN 978-0521007948.

Tests and credits.
Exercises: conditions for obtaining credit points (CP
- participation in exercises, 20% can be to apologize,
- completion of three written tests, 0-15 CP,
- completion of two programs, 5 CP.
Exam:
- written exam 0-60 CP, successful completion at least 25 CP,
- oral exam 0-20 CP, successful completion at least 5 CP.

The mandatory participation is 80%.

Subject has no prerequisities.

Subject has no co-requisities.

1. Disciplines of numerical mathematics: continuous and discrete problems, discretization order; sources of error, rounding error, computer epsilon; numerical stability.
2. Approximation and interpolation of functions: polynomial interpolation, interpolation error; least squares approximation; uniform approximation, Bernstein polynomials, spline functions; modeling curves and surfaces, Bezier curves.
3. Rootfinding for nonlinear functions: geometric approach to rootfinding; fixed-point iterations and fixed point theorem; fundamental theorem of algebra, separations and calculations of polynomial roots; Newton's method for nonlinear systems.
4. Numerical integration and derivation: numerical differentiation, Richardson extrapolation; numerical quadrature formulas, error estimation, step size control; Romberg method; Gauss formulas.
5. Numerical linear algebra: solving linear systems using LU decomposition variants, inverse matrix; eigenvalues and eigenvectors calculation, spectral decomposition; singular value decomposition, orthogonal factorization, pseudoinverse.
6. Iterative methods for solving linear systems: linear methods Jacobi, Gauss-Seidel, relaxation; nonlinear methods, steepest descent method, conjugate gradient method, preconditioning.

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

Examination | Examination | 100 | 51 | 3 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: I order to complete the credit, students submit and defend a set of solved examples assigned by the teacher. On the basis of a successfully completed credit, they can take an exam, which will consist of a practical and a theoretical part.

Show history

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

2023/2024 | (B0588A170003) Applied Sciences and Technologies | MAT | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2022/2023 | (B0588A170003) Applied Sciences and Technologies | MAT | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2021/2022 | (B0588A170003) Applied Sciences and Technologies | MAT | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B0588A170003) Applied Sciences and Technologies | MAT | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2019/2020 | (B0588A170003) Applied Sciences and Technologies | MAT | P | Czech | Ostrava | 2 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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