Why are differential equations used for expressing the laws of physics?

TL;DR

This paper explores the reasons behind the prevalent use of differential equations in physics, aiming to enhance student understanding and appreciation through an inquiry-based teaching approach.

Contribution

It provides an educational perspective on why differential equations are fundamental in physics and demonstrates how interactive teaching can improve student engagement.

Findings

Students better understand the rationale for using differential equations.

Interactive discussions enhance learning enjoyment in physics.

The approach fosters deeper conceptual comprehension.

Abstract

Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based lecture, where students and a teacher are engaged in discussion. It has two goals: (1) To help undergraduate students understand the rationale behind the use of differential equations in physics, (2) To show how meaningful and interactive presentation of mathematics can help students take pleasure in learning physics.