DEVELOPMENT OF ANALYTICAL AND ALGORITHMIC THINKING THROUGH DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING

This article examines modern methodological approaches for developing analytical and algorithmic thinking through differential equations and mathematical modeling. Differential equations represent one of the most important branches of higher mathematics because they describe dynamic processes occurring in natural sciences, engineering, economics, and technological systems. The proposed methodology integrates theoretical explanation, algorithmic reasoning, functional analysis, and practical applications to improve students’ mathematical competence. Particular attention is given to first-order and higher-order differential equations, step-by-step solution procedures, and the role of mathematical modeling in education. The study demonstrates that systematic use of analytical methods enhances logical reasoning, abstraction skills, and problem-solving abilities. The article also discusses pedagogical advantages, educational challenges, and practical recommendations for implementing this methodology in STEM-oriented learning environments.