SubjectsSubjects(version: 893)
Course, academic year 2021/2022
Applied Mathematics - N413008A
Title: Užitá matematika
Guaranteed by: Department of Mathematics (413)
Actual: from 2021
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
Is provided by: B413012
For type:  
Guarantor: Turzík Daniel doc. RNDr. CSc.
Class: Předměty pro matematiku
Examination dates   Schedule   
Annotation -
Last update: TAJ413 (05.09.2013)
The subject deals with discrete dynamical systems and difference equations which discribe simple mathematical and biological models with very complicated dynamic - chaos. The second part of the subject deals with basic algebraic structures as fields and linear spaces and shows three famous impossibilities as squaring the circle, trisecting an arbitrary angle and doubling the cube.
Aim of the course -
Last update: TAJ413 (17.12.2013)

Students learn to solve difference equations and get to know qualitative analysis of nonlinear dynamical systems with chaotic behaviour.

In the second part of subjects students get to know modern algebraic structures which are used in the proof of famous imposssibilities.

Literature -
Last update: TAJ413 (05.09.2013)

R: R. Clark Robinson: An Introduction to Dynamical Systems: Continuos and Discrete. Pearson Prentice Hall 2004, ISBN-10: 0-8218-9135-9

ISBN-13: 978-0-8218-9135-3.

R: Arthur Jones, Sidney A. Morris, Kenneth R. Pearson: Abstract Algebra and Famous Impossibilities. Springer-Verlag New York, Inc. 1991, ISBN 0-3879-7661-2

R: Mustafa R. S. Kulenovic, Orlando Merino: Discrete dynamical systems and difference equations with Mathematica, CHAPMAN&HALL/CRC,2002, ISBN 1-58488-287-5

Learning resources -
Last update: TAJ413 (05.09.2013)

Teaching methods -
Last update: TAJ413 (05.09.2013)

Lectures and seminars.

Syllabus -
Last update: TAJ413 (09.05.2011)

1. The modelling of biological systems using difference equations. The Fibonacci problem.

2. Solution of linear difference equations. Models of growing. A qualitative behavoir of the solution of difference equations.

3. Nonlinear difference equations as discrete dynamical systems. A qualitative analysis.

4. A single species population density. A two-species population, Nicholson-Bailey model.

5. Discrete predator-prey models.

6. Chaos in discrete dynamical systems.

7. Discrete Time-Delay Systems.

8. Straightedge and compass constructions, tree famous problems.

9. Algebraic numbers and their polynomials.

10. Extending fields.

11. Irredicible polynomials.

12. Constructible numbers and fields.

13. Proofs of the impossibilities.

14. Transcendencs of e and Pi.

Registration requirements -
Last update: TAJ413 (05.09.2013)

Mathematics I, Mathematice II