Thank you for your appreciation. Indeed, there are many ways to illustrate that link avoiding derivatives and integrals (I used them because I supposed that my readers are quite familiar with them).

In fact, as you probably know, you can easily substitute d with Δ in derivatives and consider quantities as differences, as in dx/dt that becomes v=Δx/Δt. When they are used inside an integral you can just skip the integral sign, assuming quantities as constants, or substitute the integral with a sum, obtaining the “arithmetic” definition of current as I=Δq/Δt.

Indeed, I am convinced that it is possible to design an entire physics course based on thermodynamics. I have not yet figured out how to do it completely, but actually there are many topics that can be introduced this way (and in many other alternative ways, in fact).