The article substantiates the important role of developing skills in constructing mathematical models of systems and processes, as well as the use of innovative computational methods that are effective in modern scientific research. Using simple examples, the authors introduce readers to the methodology of teaching the topics “New Information Operators” and “Innovative Methods of Numerical Integration”, in particular in the courses “Mathematical, Physical and Information Foundations of Industry Knowledge” and “Innovative Methods of Digitalisation of the Professional Field”. The above-mentioned educational components are studied at the Ukrainian Engineering and Pedagogical Academy in the speciality ‘‘Vocational Education (By specialisation)”. The value of these innovations lies in the fact that students get acquainted with new information operators in practice. New information operators are built depending on the type of experimental data. Currently, modern engineers use digital images, tomograms, integrals along given lines, values of functions on lines or planes, etc. as data on the technical process. Modern advances in mathematical modelling allow us to build new algorithms taking into account different types of experimental data. The article presents an algorithm for recovering a function of two variables on four or three lines, as well as on a system of mutually perpendicular lines in the computer algebra system MathCad. In addition, a cubature formula for the approximate calculation of the double integral is presented, which is effective in terms of using the input information to achieve a given accuracy. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
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