We mostly refer to the collection of ODE problems here (For English version: see links on the right.)

Please try to keep the presentation to about 10-15 minutes maximum.
It is not necessary to provide all details of elementary calculations (limits, derivatives, computing eigenvalues etc.)
In case of any questions, do not hesitate to contact me.

 

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Practicals no.1 (Oct 10, 17:20 in K9)
TOPIC: 	1. Dynamical systems -- direct link [pdf] 


Brichta O. ... Exercise 1i) and 1ii)
Dolák M. ... Exercise 4
Farský D. ... Exercise 5 (optionally, proof of Theorem 13.2)

Exercise 3 (non-connected omaga-limit set) - not completed

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Practicals no.2 (Oct 17, 17:20 in K9)
TOPIC: 	1. Dynamical systems -- direct link [pdf] 

Exercise 3 (non-connected omaga-limit set) - completed via Dulac
Example 1 - application of P.B.

Ferreira N. R.  ... Exercise 10
Fröde F. ... Exercise 13
Krupa T. ... Exercise 15

Remark on general existence of equilibria
in the interior of periodic orbits (Ex. 14)

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Practicals no.3 (Oct 31, 17:20 in K9)

M. Maleček ... state and prove Yorke's theorem. 
See page 8, Theorem 15.4 here (in Czech). Alternatively, follow
Yorke's original proof here; Lemma on page 510 need not be proven.

From the exercises on AC (a.k.a. Carathédory) solutions, see [pdf], namely:
J. Mierva  ... 1
M. Nešvera  ... 2

demo:	Lemma 16 (local uniqueness implies 
			local continuous dependence on initial condition)

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Practicals no.4 (Nov 7, 17:20 in K9)

Š. Ondřej ... state and prove Osgood's theorem, i.e. 
Theorem 13 (and Definition 7) here (in Czech).

TOPIC: 	2. Control theory -- direct link [pdf] 

J. Petr ... Exercise 1(a) and 1(b) on page 5
S. Smerčiak ... Příklad 3 zde (in Czech), see also Problem 1 here [pdf]

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Practicals no.5 (Nov 21, 17:20 in K9)

TOPIC: 	2. Control theory -- direct link [pdf] 

T. Vargicová ... Exercise 6 (page 6) -- first two matrices only
F. Vencl ... Exercise 7 (page 6) -- also compute the characteristic polynomial of A
D. Vitner ... prove Theorem 18.2 (on observability of linear systems)

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Practicals no.6 (Nov 28, 17:20 in K9)

Example - quadratic regulator.

M. Zelko ... Example 3 (on page 24) -- only discuss the maximum principle
	(to be finished)
D. Farský ... Exercise 21 (page 29)

From additional problems from control theory, see [pdf], please prepare the following:

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Practicals no.7 (Dec 5, 17:20 in K9)

From additional problems from control theory, see [pdf], please prepare the following:
M. Nešvera ... Problem 5 (to be finished)
O. Brichta ... Problem 3

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Practicals no.8 (Dec 12, 17:20 in K9)

From collection of problems on control theory ([pdf]):
F. Fröde ... Example 6 (page 26)
J. Mierva ... Exercise 22 (page 29), only case (ii)

Example - saddle-note bifurcation in 2d

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Practicals no.9 (Dec 19, 17:20 in K9)
(T. Bárta)

From collection of problems on centre manifolds ([pdf])

demo:	Examples 1, 2
class:	exercises 5,6,7,11

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Practicals no.10 (Jan 9, 17:20 in K9)

Additional problems on centre manifolds ([pdf])