I’ve been meaning to get back to your comments linked above — the connections you observed to finite difference calculus, ordinary and partial differential equations, and differential geometry are very apt — but preparing the ground for a smooth transition to differential logic takes time, plus I needed to deal with the details of the logical graph duality I’ve been wanting to give their due for decades.
The flat out fastest key to the highway of differential logic is still the Casual Introduction I wrote for Part One of Differential Propositional Calculus. It affords direct access to the basic intuitions and motivations of the subject but stops short of the syntactic mechanics needed to really take off. The jump from that point to the more aggressive approaches of Differential Logic and Differential Logic and Dynamic Systems has long been a challenge. I went looking for materials to bridge the gap and was pleased to find a few old writings I had almost forgotten but wrote when I myself was passing through a similar transition. Perhaps one of those will help the intrepid reader hit the ground running in this field.
I’ll take up one of those pieces next time.