APPLICATIONS OF DIFFERENTIAL EQUATIONS IN PHYSICS

Abstract

Differential equations play a fundamental role in the formulation and analysis of physical phenomena. They provide a mathematical framework for describing the relationships between changing quantities and their rates of change in various physical systems. This article explores key applications of differential equations in classical mechanics, electromagnetism, thermodynamics, quantum mechanics, and fluid dynamics. By modeling physical laws such as Newton’s laws of motion, Maxwell’s equations, and the Schrödinger equation through differential equations, scientists can predict system behaviors, analyze stability, and solve complex problems. The paper also highlights the importance of both ordinary and partial differential equations and discusses analytical and numerical methods used to solve them. This study underscores the essential role of differential equations as a bridge between mathematics and physics.