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• The theory of functional equations in high school education

  345-360

  Dorottya Bessenyei

  Views:

  42

  In this paper, we are going to discuss some possible applications of the theory of functional equations in high school education. We would like to line up some problems, the solution of which by functional equations are mostly not new results – they have also been treated in [1] and [2] –, although their demonstrations in high school can show a new way in teaching of talented students. The area of the rectangle, the calculating method of compound interest, binomial coefficients, Euler's formula, the scalar product and the vector product of vectors – we are looking for the reasons behind the well-known formulas. Finally, we are going to give a functional equation in connection with mean values. It can be understood easily, but its solution is beyond the high school curriculum, so we advise this part only to the most talented students.

• Sequenced problems for functional equations

  179-192

  Zsolt Ádám

  Károly Lajkó

  Gyula Maksa

  Fruzsina Mészáros

  Views:

  11

  There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y 2 R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education.

• A KöMaL problem in a new view

  191-201

  Pál Péter Dályay

  Views:

  12

  The object of this paper is finding the general solution f : R^3 → R of the system of functional equations (1) valid for all x, y, z, t ϵ R. First f is expressed by a function of one variable which satisfies a system of two functional equations.This system is resolved by using an algebraic reformulation of the problem in terms of orbits and transversals. Finally the general solution of (1) is obtained.

• Erratum to the paper "The theory of functional equations in high school education" Teaching Mathematics and Computer Science 10/2 (2012), 345-360

  145

  Dorottya Bessenyei

  Views:

  12

  A correction is necessary in subsection 2.5. although this does not affect the truth of the main formula.