SubjectsSubjects(version: 953)
Course, academic year 2021/2022
Mathematics B: Seminar - B413014
Title: Výběrový seminář k Matematice B
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: summer
Points: summer s.:2
E-Credits: summer s.:2
Examination process: summer s.:
Hours per week, examination: summer s.:0/2, C [HT]
Capacity: unknown / unlimited (unknown)
Min. number of students: unlimited
State of the course: taught
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: Borská Lucie RNDr. Ph.D.
This subject contains the following additional online materials
Annotation -
The seminar deepens students knowledge gained in lectures and exercises in Mathematics B. The main content of the course is working with gifted students, the emphasis is on solving more complex and application examples from different parts of Mathematics B. The application examples motivate students to expand their theoretical knowledge.
Last update: Borská Lucie (14.02.2022)
Aim of the course -

The outcomes are motivated by the effort to supplement and expand the teaching of the newly accredited course Mathematics B so that future talented students will acquire the same knowledge as students of the current subject Mathematics B taught for students of the field of study Chemistry.

Last update: Borská Lucie (14.02.2022)
Literature -

R: Klíč a kol.: Matematika I ve strukturovaném studiu, skripta, VŠCHT Praha, 2007, ISBN: 978-80-7080-656-2

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

R: Míčka a kol.: Sbírka příkladů z matematiky, skripta, VŠCHT Praha, 2002, ISBN 80-7080-484-X

A: Děmidovič: Sbírka úloh a cvičení z matematické analýzy, Fragment Praha, 2003, ISBN 80-7200-587-1

A: Porubský: Fundamental Mathematics for Engineers, Vol.I, VŠCHT, 2001, ISBN: 80-7080-418-1

Last update: Borská Lucie (15.02.2022)
Learning resources -

Matematika s programem Mathematica a Maple -

E-sbírka Výběrový seminář k Matematice B - see e-learning

Last update: Axmann Šimon (15.02.2022)
Teaching methods -

Seminars. Students are encouraged to study independently and present the results obtained.

Last update: Borská Lucie (14.02.2022)
Requirements to the exam -

The basis for assessment will include a final project

Last update: Borská Lucie (14.02.2022)
Syllabus -

1. Linear vector spaces, linear maps, compound mapping, inverse mapping.

2. Eigenvalues, eigenvectors, spectral decomposition and singular decomposition of matrices.

3. Geometry in plane and space.

4. Metric, norm, finite and infinite dimensional spaces, examples.

5. Newton's method for systems of more than two nonlinear equations.

6. Lagrange multiplier theorem.

7. Least squares method.

8. Variation of constants for linear second order differential equations

9. Autonomous systems of linear differential equations with constant coefficients.

10. Triple integral and its geometric meaning.

11. Numerical series and convergence criteria.

12. Power series. Pointwise, absolute and uniform convergence.

13. Introduction to dynamical systems, simple models of biological and chemical processes.

14. Deterministic chaos.

Last update: Axmann Šimon (15.02.2022)
Registration requirements -

Mathematics A

Last update: Axmann Šimon (15.02.2022)