SubjectsSubjects(version: 893)
Course, academic year 2021/2022
Selected chapters in Mathematics - B413012
Title: Vybrané kapitoly z matematiky
Guaranteed by: Department of Mathematics (413)
Actual: from 2020
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Turzík Daniel doc. RNDr. CSc.
Axmann Šimon Mgr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : N413031
Examination dates   Schedule   
Annotation -
Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)
Students will be acquainted with the theory of function series and they will deepen knowledge of linear algebra. Moreover, they will learn some basic concepts of the functional analysis and the Fourier series.
Aim of the course -
Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)

The students will deepen knowledge in the following areas:

1. Theory of series including function series

2. Linear algebra, namely orthogonal projection, least square solution, eigenvalues and eigenvectors, singular decomposition of matrices

3. Basis knowledge of functional analysis

4. Fourier series

All theoretical concepts will be illustrated by simple examples and exercises

Literature -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)

R: J. Lukeš: Zápisky z funkcionální analýzy, Univerzita Karlova v Praze, Nakladatelství Karolinum, 2002,ISBN 80-7184-597-3

R: Turzík a kol.: Matematika II ve strukturovaném studiu, skripta, VŠCHT Praha, 2005, ISBN 80-7080-555-2

R: J. Duintjer Tebbens et al.: Analýza metod pro maticové výpočty. Základní metody, MatfyzPress, 2012, ISBN 978-80-7378-201-6

R: Z. Došlá, P. Liška: Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách, Grada Publishing, 2014, ISBN 80-2479-206-0

A: R. A. Horn, C. R. Johnson: Matrix Analysis. Cambridge Universitz Press 1999 (6. vydání). ISBN 0-521-38632-2

Learning resources -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)

Teaching methods -
Last update: Kubová Petra Ing. (01.05.2019)

Lectures, exercises

Syllabus -
Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)

1. Convergence of sequences and series of numbers, convergence and absolute convergence, criteria.

2. Convergence of series and sequences of functions, convergence and uniform convergence, criteria.

3. Power series, radius of convergence. Taylor series.

4. Fourier series.

5. Normal equations, their solutions, and applications.

6. Condition number. Orthogonal matrices, orthogonal transformations

7. Decomposition and iterative methods in numerical linear algebra.

8. Eigenvalues ​​and eigenvectors. Singular values​​, singular value decomposition.

9. Normed vector spaces. Banach spaces R^n, L^p, l^p, C^k.

10. Scalar product, Hilbert spaces, orthogonal systems.

11. Linear operators, functionals, dual space.

12. Eigenfunctions of linear operators. Spectral theory in Hilbert spaces.

13. Mathematical description of quantum mechanics.

14. Application of Fourier series and spectral theory to the basic problems in quantum mechanics.

Registration requirements -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)

Mathematics I, Mathematics II or Matematika I, Matematika II