By halfway through this, I will confess to having to admit the maths had the better of me, and calculus will need to remain the obscured art it has been for some time. I found it very difficult at school, so I suspect this is more me than the writing.
I did enjoy the history here, and I know understand much better how mathematics advances were essential to physics advancing, and also how they have laid the basis for so much modern technology. Maths is about modelling how things work, an approach I still wish I had had more embedded in my teaching. And by using abstractions, we can model things that we can't easily imagine (or measure - it was a revalation to me to realise how difficult calculating the length of a curve is when you can't just use string).