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1
Content available remote Rola matematyki w nowoczesnej edukacji - Polskie szanse cywilizacyjne w Europie
Sokała M.
Zeszyty Naukowe Akademii Marynarki Wojennej
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2011
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R. 52 nr 187A
271--281
PL
Zarówno w debacie eksperckiej, jak i w publicystyce możemy znaleźć liczne dowody na to, że matematyka stanowi przedmiot uznawany za szczególnie trudny. Stąd próby jej pomijana lub marginalizowania, przynajmniej częściowego, w naszym systemie edukacyjnym. Tymczasem właściwe pytanie o nauczanie matematyki nie powinno brzmieć "czy", lecz "po co" I w konsekwencji ,jak". Prawidłowa (tzn. elastyczna i skuteczna) dydaktyka matematyki warunkuje bowiem jakość całego procesu kształcenia, ta zaś - poziom narodowych szans cywilizacyjnych.
EN
Both in an experts' debate and in journalistic texts, we can find ample evidences that mathematics is the subject considered to be particularly difficult. 8ecause of that, there are many attempts to bypass or marginalize it, at least partly, in our educational system. We should not discuss if the leaching of mathematics is necessary. What we should discuss is how to and what a teacher. The correct (Le. flexible and effective) mathematical education determines the quality f whole educational process and consequently our national opportunities in the sphere of the civilization.
2
Content available remote Solution of 2D non-homogenous wave equation by using polywave functions
Sokała M.
Computer Assisted Mechanics and Engineering Sciences
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2009
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Vol. 16, No. 3/4
209-221
EN
The paper presents a specific technique of solving the non-homogenous wave equation with the use of Trefftz functions for the wave equation. The solution was presented as a sum of a general integral and a particular integral. The general integral was expressed in the form of a linear combination of Trefftz functions for the wave equation. In order to obtain the particular integral polywave functions were used. They were generated by using the inverse operator L -1 of the equation taking into consideration the Trefftz functions.
3
Content available remote 2D wave polynomials as base functions in modified FEM
Maciąg A., Maciejewska B., Sokała M.
Computer Assisted Mechanics and Engineering Sciences
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2008
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Vol. 15, No. 3/4
265-278
EN
The paper presents solutions of a two-dimensional wave equation by using Trefftz functions. Two ways of obtaining different forms of these functions are shown. The first one is based on a generating function for the wave equation and leads to recurrent formulas for functions and their derivatives. The second one is based on a Taylor series expansion and additionally uses the inverse Laplace operator. Obtained wave functions can be used to solve the wave equation in the whole considered domain or can be used as base functions in FEM. For solving the problem three kinds of modified FEM are used: nodeless, continuous and discontinuous FEM. In order to compare
4
Content available remote Solutions of Two-Dimensional Wave Equation using some Form of the Trefftz Functions
Sokała M.
Computational Methods in Science and Technology
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2008
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Vol. 14, nr 2
111-122
EN
The paper presents a specific technique to generate the Trefftz functions for the two-dimensional wave equation. The obtained functions are used to determine approximate solutions of some tested problems. The accuracy of the method is discussed.
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