This article describes how to do simple temperature measurement with a Raspberry Pi, and I2C analog-to-digital converter, and a thermistor.
My article on calculus of variations assumed without explanation the basic form of the Euler-Lagrange equation. This article attempts to demonstrate how an Euler-Lagrange equation arises, by solving a variational problem algebraically using Maple.
The use of integrating factors is a well-known method for turning an intractable differential equation into an integration problem (which may itself turn out to be intractable, but we live in hope). The method is usually described in textbooks and lectures with a fair amount of hand-waving. This article attempts to describe it in detail, with none of the difficulties left out.
There is a tabular method for organizing integration computations which require repeated application of the integration-by-parts formula. It is seldom taught, which is a shame: it hugely reduces the algebraic complexity of the problem.
Make an auxiliary LCD display for a computer that displays data sent to it over a USB connection. Ready-made devices of this sort are widely available, but it's more fun to build your own.