The Integral and Differential Form of Mathematical Physics Equations—reflections on a European Olympiad in Physics Competition Experimental Problem

Mathematical physical equations are a series of partial differential equations that describe objective physical laws. In the 2021 European Olympic Physics Competition (2021EuPhO), there was an experimental question of “heat conduction in a thin rod” which required calculating the relevant parameters of the rod and was closely related to mathematical physics equations. In the original solution to the problem, the proposer used Simpson method to take an average of five temperature sampling points on the thin rod and calculating the average temperature to approximate the overall temperature change of the rod over time. This question is very similar to the thermal diffusion problem in Mathematical Physics Methods, so we sort out this topic based on the thermal diffusion problem in mathematical equations. Taking this question as an opportunity, we analyze the integral form, differential form of mathematical equations and the applicability of Simpson integration method.