International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

In this paper, the infinite numbers and functions are introduced and applied in modeling physical and mathematical systems and processes, where infinity somehow appears, i.e. infinite ladder electrical networks and systems instability analysis, series of numbers and limits calculation. Infinite numbers are defined as limits of complex functions that tend to infinity. Using these numbers it is possible to calculate the extended Laplace transform across the whole frequency spectrum as well as the extended bilateral Laplace transform, where the corresponding integral does not converge. Furthermore, the derivatives/integrals of the infinite number functions are determined. Using infinite numbers certain mathematical problems can be analysed and calculated, as well as problems in Physics and Engineering, where infinity appears, can be easily modeled and solved.

Laplace’s transformation is an important chapter of Mathematical Analysis. At present it is widely used in various problems of signal theory, physics, mechanics, electro – techniques and economics. Laplace’s transformation is the simplest and most economical method that leads directly to the required resolution of many of the various technical problems that arise when solving them. In this paper we will become acquainted with the basic concepts of operational mathematics and its application in economy. Not many analytic solutions exist for present discounted value problems but by using Laplace transform we can deduce some of the closed form solutions quite easily. There will be shown the connection between the current discounted value in finance and Laplace transformation.