|Volume XXI , issue 1 ( 2018 )||back|
|Substitutions in differential equations as a geometry of their symmetries||1$-$14|
We enlighten a geometrical background for familiar substitutions in certain ordinary differential equations. We explain how the existence of a symmetry of a differential equation provides a change of coordinates (i.e., a substitution) in which the initial equation becomes in quadrature form.
Keywords: Ordinary differential equation; symmetries; substitution.
MSC Subject Classification: 97I70, 97I40
MathEduc Subject Classification: I75
|Relating procedural and conceptual knowledge||15$-$28|
Relating procedural and conceptual mathematical knowledge is a very important educational goal that is difficult to attain. However, research has evidenced that some progress towards achieving this goal can be made. This contribution briefly reviews some of the main outcomes of research in this area, focusing on relating these knowledge types with technology, particularly that based upon a computer algebra system.
Keywords: Conceptual knowledge; procedural knowledge; technology.
MSC Subject Classification: 97C30
MathEduc Subject Classification: C34
|Pedagogical work of Mihailo PetroviĆ Alas (1868--1943)||29$-$37|
The aim of this text is to look back on the creativity of Mihailo Petrović Alas, a well-known Serbian mathematician and the founder of the Belgrade Mathematical School, on the occasion of his 150th anniversary. The text deals with his contributions to mathematical teaching, as well as the influence of his pedagogical ideas on the development of mathematics in Serbia until these days.
Keywords: Mihailo Petrović Alas
MSC Subject Classification: 01A70, 97-03
MathEduc Subject Classification: A30
|Hybridization of classical inequalities with equivalent dynamic inequalities on time scale calculus||38$-$52|
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.
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|
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