SubjectsSubjects(version: 855)
Course, academic year 2019/2020
Mathematics III - N413031
Title: Matematika III
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
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.
Janovská Drahoslava prof. RNDr. CSc.
Class: Předměty pro matematiku
Is interchangeable with: B413012
Examination dates   Schedule   
This subject contains the following additional online materials
Annotation -
Last update: Janovská Drahoslava prof. RNDr. CSc. (29.08.2013)
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 and vector analysis.
Aim of the course -
Last update: TAJ413 (05.09.2013)

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. Basics of vector analysis: Hamilton operator "nabla" and operators grad, div, rot. Green's formulas.

All theoretical concepts will be illustrated by simple examples and exercises

Literature -
Last update: Janovská Drahoslava prof. RNDr. CSc. (29.08.2013)

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: A. Klíč, M. Dubcová: Základy tenzorového počtu s aplikacemi, VŠCHT Praha, 1998.

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. (19.01.2017)

Teaching methods -
Last update: Janovská Drahoslava prof. RNDr. CSc. (29.08.2013)

Lectures, exercises

Syllabus -
Last update: Janovská Drahoslava prof. RNDr. CSc. (29.08.2013)

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. Orthogonal matrices, orthogonal transformations.

5. Normal equations, their solutions, and applications.

6. Matrix decompositions LR, QR.

7. Eigenvalues ​​and eigenvectors.

8. Singular values​​, singular value decomposition.

9. Norm and scalar product in function spaces C^k(Ω), L^2(Ω). Banach and Hilbert spaces. Orthogonal systems.

10. Linear functionals.

11. Linear and nonlinear operators.

12. Eigenvalues ​​and eigenfunctions of linear operators.

13. Basics of vector analysis: Hamilton operator "nabla" and operators grad, div, rot.

14. Gauss theorem. Green's formulas.

Registration requirements -
Last update: Janovská Drahoslava prof. RNDr. CSc. (15.02.2018)

Mathematics I, Mathematics II or Matematika I, Matematika II

Teaching methods
Activity Credits Hours
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1,5 42
Příprava na zkoušku a její absolvování 1,5 42
Účast na seminářích 1 28
5 / 5 140 / 140
Coursework assessment
Form Significance
Regular attendance 40
Examination test 60