Mathematics as the language of physics

TL;DR

This paper examines the importance of mathematical rigor in physics, focusing on the conditions under which common mathematical expressions are valid, exemplified through the derivation of isothermal compressibility.

Contribution

It highlights the significance of mathematical rigor in physics calculations and analyzes the validity conditions of frequently used expressions.

Findings

Clarifies the conditions for the validity of mathematical expressions in physics

Emphasizes the importance of rigor in mathematical methods for physics students

Provides an example involving isothermal compressibility

Abstract

Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical expressions are valid can be of great importance in some physical circumstances. Here one such expression, which figures frequently in the manipulations leading to the isothermal compressibility appearing in formulae, is examined as an illustrative example.