Using Mathcad in the design of professionally oriented mathematical analysis assignments in technical universities

Abstract

In the context of the rapid modernization of higher technical education and the increasing demands on the quality of engineering training, the issue of improving teaching methods for fundamental disciplines, particularly mathematical analysis, becomes especially relevant. Traditional approaches, focused on the assimilation of abstract theoretical concepts and the development of routine computational skills, often fail to provide students with a holistic understanding of the role of mathematics in their future professional activities. This results in reduced motivation, superficial learning, and a gap between theoretical knowledge and the ability to apply it to solve real engineering problems. Bridging this gap requires the development and implementation of innovative teaching technologies that promote the integration of mathematical training with specialized disciplines. One of the most promising directions is the use of modern computer algebra systems, which allow shifting the focus from lengthy calculations to problem formulation, mathematical model analysis, and interpretation of results in a professional context. In this regard, the Mathcad system represents a powerful and intuitive tool, offering wide opportunities for symbolic and numerical calculations as well as data visualization. However, simply using the software as a «calculator» does not yield the desired pedagogical effect. Purposeful development of didactic materials - professionally-oriented assignments that naturally incorporate Mathcad into the problem-solving process - is necessary. This study was based on a pedagogical experiment conducted at a technical university among second-year students studying the discipline «Mathematical Analysis». Two groups of engineering students participated: a control group (n=32) and an experimental group (n=34). The control group was taught using traditional methods, including lectures, classroom problem-solving, and independent textbook study. In the experimental group, teaching methods were modified through the integration of Mathcad. A special set of professionally-oriented assignments was developed for this group, covering key areas of mathematical analysis such as differential and integral calculus, differential equations, and series. Each task described a specific engineering problem (for example, calculating beam deflection under load, determining the thermal field in a plate, or analyzing transient processes in an electrical circuit), the solution of which required not only applying the relevant mathematical tools but also using Mathcad's computational, plotting, and parametric analysis functions. The research materials included entry-level testing data, results of mid-term assessments, final exam scores, and student survey responses aimed at evaluating motivation, engagement, and understanding of the practical significance of the subject. The primary research method was comparative analysis of quantitative and qualitative indicators of student performance in the control and experimental groups. To assess the statistical significance of academic performance differences, mathematical statistics methods were applied, specifically the Student's t-test for independent samples. The results of the pedagogical experiment demonstrated significant improvements in the experimental group's learning outcomes. The average score in the final test on «Integral Calculus» was 4.42 compared to 3.87 in the control group, with a reduction in standard deviation from 0.83 to 0.51, indicating more consistent knowledge levels. The percentage of successfully completed advanced problems increased from 45,3% to 71,8%. The average time for solving complex problems decreased from 45,6 to 28,3 minutes. Surveys showed increased interest in the subject (from 3.15 to 4.58 points), better understanding of its practical importance (from 2.98 to 4.71), and higher confidence levels (from 3.05 to 4.49). For visualization tasks, the percentage of correct graphical interpretations rose from 35,8% to 89,2%, while the qualitative evaluation of understanding increased from 4.1 to 8.7 points on a 10-point scale. Discussion of the results confirms that integrating Mathcad into professionally-oriented assignments not only automates computations but also promotes the development of research competencies, deeper understanding, and increased student motivation. Reduced time spent on calculations allows students to focus on analysis and interpretation, while visualization enhances intuitive comprehension. The findings have practical significance for modernizing teaching practices in technical universities and recommend the approach for other disciplines as well. This supports the integration of fundamental and specialized training, fostering competencies that meet labor market requirements.