* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 470-8724/01 | |||||
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Number of ECTS Credits Allocated | 4 ECTS credits | |||||

Type of Course Unit * | Compulsory | |||||

Level of Course Unit * | First Cycle | |||||

Year of Study * | First Year | |||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

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

Summary | ||||||

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. | ||||||

Learning Outcomes of the Course Unit | ||||||

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. | ||||||

Course Contents | ||||||

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. | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

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

DOSTÁL, Z., VONDRÁK, V.: Lineární algebra. Elektronická skripta VŠB-TU Ostrava, http://mi21.vsb.cz | ||||||

Recommended Reading: | ||||||

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

ŠINDEL, L.: Lineární algebra v příkladech. Skripta VŠB-TU Ostrava, 1999. | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Tutorials | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

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

Credit | Credit | 30 | 10 | |||

Examination | Examination | 70 | 21 |