Mathematics as the language of physics

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.