Subjects

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Applied Mathematics - N413008

Title:	Užitá matematika
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2013 to 2013
Semester:	winter
Points:	winter s.:5
E-Credits:	winter s.:5
Examination process:	winter s.:
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Level:
Note:	course can be enrolled in outside the study plan enabled for web enrollment

Guarantor:	Turzík Daniel doc. RNDr. CSc.

Examination dates Schedule

Annotation -

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.

Last update: VED413 (04.09.2013)

Aim of the course -

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.

Last update: TAJ413 (17.12.2013)

Literature -

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

Last update: VED413 (04.09.2013)

Teaching methods -

Lectures and seminars

Last update: VED413 (04.09.2013)

Syllabus -

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.

Last update: TAJ413 (09.05.2011)

Learning resources -

http://www.vscht.cz/mat/UM/CviceniUM.html

Last update: VED413 (04.09.2013)

Registration requirements -

Mathematics I, Mathematice II

Last update: VED413 (04.09.2013)

Teaching methods
	Activity	Credits	Hours
	Konzultace s vyučujícími	0.5	14
	Účast na přednáškách	1	28
	Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi	1	28
	Příprava na zkoušku a její absolvování	1.5	42
	Účast na seminářích	1	28
		5 / 5	140 / 140

Coursework assessment
Form	Significance
Regular attendance	10
Examination test	50
Continuous assessment of study performance and course -credit tests	40