The scientific activity of the Department of Higher Mathematics and Systems Analysis (No. 405) is aimed at developing modern mathematical methods and their effective application for solving complex applied problems in mechanical engineering, aviation, and aerospace industries. The department actively combines fundamental research with applied development, implemented within the framework of state-funded topics and research projects at various levels.
The department's scientific research areas include: development of an integrated technology for creating wear-resistant coatings based on NiTi and TiAl intermetallics on titanium alloy parts.
A key area of scientific work is the execution of departmental research topics. In 2021–2023, the topic "Creation of a Mathematical Apparatus for Solving Applied Problems" (0122U201064) was implemented, laying the theoretical foundations for modeling complex physical processes and improving approaches to engineering systems analysis. Its logical continuation is the topic "Development and Application of Constructive Mathematical Methods for Solving Applied Problems" (0124U001351, 2024–2026), which focuses on creating efficient algorithms and practical tools for engineering applications.
Applied scientific projects aimed at solving relevant problems of modern technology play a special role in the department's activities. In particular, the project "Optimal Design of Adhesive Joints in Aerospace Composite Structures" (D405-6/2022-P, 0122U001784) was carried out in 2022–2023 under the supervision of Professor Serhii Kuriennov. Within this project, mathematical models and optimization methods were developed to increase the reliability and strength of composite joints widely used in aviation.
In 2024–2025, the department participated in the project "Development of Technology and Equipment for Cold Gas Dynamic Spraying" (No. 0124U000553), with Head of the Department Nina Savchenko serving as one of the key researchers. The study focused on creating advanced coating technologies for the restoration and strengthening of machine parts and aircraft structures.
The department pays significant attention to supporting young scientists through a series of promising projects. Specifically, the project "Development of an Integrated Technology for Creating Wear-Resistant Coatings Based on NiTi and TiAl Intermetallics on Titanium Alloy Parts" (D204-1/2025-M, 2025–2027), supervised by Nina Savchenko, aims at creating new materials with enhanced wear resistance. Another project, "Innovative Cold Gas Dynamic Spraying Technologies for Rapid Production and Repair of Critical Aircraft Components" (D204-3/2026-M, 2026–2028), is focused on implementing fast and efficient restoration technologies for complex technical products.