Global Journal of Researches in Engineering, I: Numerical Methods, Volume 23 Issue 1

Figure 9: Curves of equal loudness _y, dB and a curve approximating them rjad( x) , Hertz From the materials presented in the figures, it can be seen that for a given number of points, the approximation is satisfactory. IV. C onclusions Differential integral functions, this is the Riemann-Liouville differential integral, written in a convenient form, as a function of two variable s 7 7 There may be other parameters, for example, integration limits, constants, etc. : the usual argument x and the parameter k, which sets the multiplicity of the integral or the order of the derivative. These functions allow you to calculate the desired integral or derivative by substituting the parameter k into the established formula. The formula does not change, only one parameter changes. Classical tables of integrals and differentials are not required. Only tables of pre-prepared formulas of differential functions are used, which can be represented in simple calculations in the form of icons, and in the form of SL (x, k) functions in computer programs written in programming languages such as VBasic, C++, Excel, MathCad, Python, etc. These differential integral functions are of great practical importance, for example, they allow us to approximate a certain given function in the vicinity of the desired point (by the type of decomposition into a Taylor, Maclaurin, Fourier series or Z transformation) or on a segment. At the same time, the conditions of equality of not only the function itself, but also the selected derivatives and differentials, integer and fractional, are observed at the desired approximation points themselves. Examples of approximation of some elementary functions are shown, for example, using a standard polynomial. It is also possible to approximate trigonometric, power functions and their combinations. To simplify working with differential integral functions, they can be represented in two forms: for a graphic image-as a function with angle brackets, and for writing in the program text-as a function SL (x, k) of two or more arguments (Application B). © 2023 Global Journals Global Journal of Researches in Engineering Volume XxXIII Issue I Version I 21 Year 2023 ( ) I Application of Differentialintegral Functions