SubjectsSubjects(version: 954)
Course, academic year 2023/2024
Mathematics III - N413031
Title: Matematika III
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
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 [HT]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
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   
Annotation -
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.
Last update: Janovská Drahoslava (29.08.2013)
Aim of the course -

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

Last update: TAJ413 (05.09.2013)
Literature -

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

Last update: Janovská Drahoslava (29.08.2013)
Learning resources -

Last update: Axmann Šimon (19.01.2017)
Teaching methods -

Lectures, exercises

Last update: Janovská Drahoslava (29.08.2013)
Syllabus -

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.

Last update: Janovská Drahoslava (29.08.2013)
Registration requirements -

Mathematics I, Mathematics II or Matematika I, Matematika II

Last update: Janovská Drahoslava (15.02.2018)
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