Gurantor department | Department of Applied Mathematics | Credits | 4 |

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

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2015/2016 | Year of cancellation | 2020/2021 |

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

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

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

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

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

Many engineering problems lead to solution of large-scale systems of linear equations. The aim of this course is to introduce fundamental notions of linear algebra and relate them to applications in electrical engineering. First we shall learn how to solve real and complex systems of linear equations by Gauss elimination method. The systems arises in the analysis of electrical circuits. In an intuitive manner we shall introduce notions such as base of a vector space, linear transformation and using them we will formulate basic linear problems. In the second part of the course, we shall focus on quadratic forms, which are closely related e.g. to electrical potential energy. Further we shall study orthogonality of functions, on which e.g. Fourier analysis of signals rely. Finally, we shall introduce spectral theory with applications to analysis of resonances.

Lectures

Tutorials

Linear algebra is a basic tool of formulation and effective solution of technical problems. The students will get knowledge of basic concepts and computational skills of linear algebra.

GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.

GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.

2 tests (15 pts.)
Homework (15 pts.)

There are no further requirements.

Subject has no prerequisities.

Subject has no co-requisities.

1. Systems of linear equations.
2. Gaussian elimination.
3. Matrix calculus, inverse matrices.
4. Vector spaces.
5. Base and solvability of systems of linear equations.
6. Linear maps.
7. Bilinear forms, determinants.
8. Quadratic forms.
9. Orthogonality, orthogonal projection, the method of least squares.
10. Eigenvalues and eigenvectors.

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 | 30 | 10 |

Examination | Examination | 70 | 21 |

Show history

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

2019/2020 | (B3968) Applied Sciences and Technologies | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2018/2019 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 1 | Compulsory | study plan |

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