Volume XXI , issue 1 ( 2018 )back
Substitutions in differential equations as a geometry of their symmetries1$-$14
Jelena Katić
University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia


We enlighten a geometrical background for familiar substitutions in certain ordinary differential equations. We explain how the existence of a symmetry of a differential equation provides a change of coordinates (i.e., a substitution) in which the initial equation becomes in quadrature form.

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Keywords: Ordinary differential equation; symmetries; substitution.

MSC Subject Classification: 97I70, 97I40

MathEduc Subject Classification: I75

Relating procedural and conceptual knowledge15$-$28
Djordje M. Kadijevich
Institute for Educational Research, Dobrinjska 11/III, 11000 Belgrade, P.O.B. 546, Serbia


Relating procedural and conceptual mathematical knowledge is a very important educational goal that is difficult to attain. However, research has evidenced that some progress towards achieving this goal can be made. This contribution briefly reviews some of the main outcomes of research in this area, focusing on relating these knowledge types with technology, particularly that based upon a computer algebra system.

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Keywords: Conceptual knowledge; procedural knowledge; technology.

MSC Subject Classification: 97C30

MathEduc Subject Classification: C34

Pedagogical work of Mihailo PetroviĆ Alas (1868--1943)29$-$37
Vojislav Andrić
Valjevo High School, Valjevo, Serbia


The aim of this text is to look back on the creativity of Mihailo Petrović Alas, a well-known Serbian mathematician and the founder of the Belgrade Mathematical School, on the occasion of his 150th anniversary. The text deals with his contributions to mathematical teaching, as well as the influence of his pedagogical ideas on the development of mathematics in Serbia until these days.

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Keywords: Mihailo Petrović Alas

MSC Subject Classification: 01A70, 97-03

MathEduc Subject Classification: A30

Hybridization of classical inequalities with equivalent dynamic inequalities on time scale calculus38$-$52
Muhammad Jibril Shahab Sahir
Department of Mathematics, University of Sargodha, Sub-Campus Bhakkar, Pakistan and GHSS, 67/ML, Bhakkar, Pakistan


The aim of this paper is to present some classical inequalities and to form their symmetric dynamic versions on time scale calculus. We also present that their symmetric dynamic versions on time scales are equivalent.

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Keywords: Bernoulli's inequality; Radon's inequality; Rogers-Höl\-der's inequality; Schlömilch's inequality; the weighted power mean inequality; time scales

MSC Subject Classification: 97H30, 26D15

MathEduc Subject Classification: H35

Bernd Zimmermann (Obituary)53
Lenni Haapasalo
Family friend and colleague Professor at the University of Eastern Finland



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MSC Subject Classification:  

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