Роль диференціальних рівнянь у прогнозуванні та аналізі фізичних процесів

Abstract

The paper considers the application of differential equations as a primary mathematical tool for modeling physical processes. It is shown that discrete or intuitive approaches often lead to paradoxical or incorrect results, whereas a continuous description based on differential equations allows accounting for the rate of change of the system and its stabilizing mechanisms. Examples of heat transfer, oscillatory systems, and electrical circuits are presented, demonstrating how the use of differential equations eliminates inconsistencies inherent in discrete analysis and provides physically meaningful predictions.