Maple tools for the Kurzweil integral

Abstract

then the resulting integral is equivalent to an integral introduced by Perron in 1915. If the definition is formulated directly rather than through differential equations then it amounts to a small but ingenious modification of the Riemann definition. Henstock [6], [7], [8], [10], [9] rediscovered Kurzweil’s approach and made further contributions. Today this integral is known under various names, such as Kurzweil’s, Henstock’s, Kurzweil-Henstock’s and the generalized Riemann integral. We shall refer to it as Kurzweil’s integral. It is becoming popular and widely used. McLeod’s book [16] is intended for (university) teachers, Bartle’s book [2] and Gordon’s publication [5] are aimed at graduate level, however with different focuses. Bartle believed that Kurzweil’s integral should become the integral. Lanzhou lectures by Lee Peng Yee [14] are also directed at an advanced audience. Muldowney [17] treats the subject in an abstract setting. In contrast, [3] and [4] contain an introduction to the Kurzweil