Mathematics for digital signal processing: series and integrals of Fourier in professional training

The article presents the features of applying mathematical knowledge in the professional training of modern specialists in digital production transformation. Accordingly, the article investigates the methodological strategies and practices of using the Fourier series in the educational process based on the developed pedagogical system, “Constructive-interpretive concept of the development of mathematical knowledge and thinking of a future engineer”, with the integrative use of digital technologies, including visualisation. The integrative use of the Fourier series and digital technologies contributes to the development of a system of professionally significant intellectual qualities in a future specialist, among which the relevant ones are the abilities to: modeling, finding solutions, calculation (in the sense of complex calculations), interpretation, construction, anticipation (forecasting), representation, analysis and synthesis, innovative activity, conceptualization, scientificization. The professionalisation of specialists through a practically oriented study of mathematics and the application of digital technologies, as well as the mastery of interconnected processes such as mathematisation, cognitivisation, digitalisation and scientificisation of production in the technosphere, management, design and monitoring are considered systemic factors in the digital transformation of production. These factors are also conditions for increasing its efficiency, competitiveness, environmental friendliness and innovative development. According to the results of the conducted pedagogical research, the presence of difficulties in solving problems of applied content was determined in future specialists of engineering specialties, which are minimized when using digital technologies and the practical orientation of mathematical knowledge. At the final stage of the study, the positive dynamics of the results of educational achievements were determined, aimed at the development of special mathematical knowledge and the formation of creative abilities, as well as their practical application.