This is a book I’ve wanted for a long time. Being many years out of college, and having forgotten everything I once knew about theoretical physics (which, sadly, was not nearly as much as I thought I knew), I have been looking for a way to refresh my knowledge. This little book is that way.
It’s intended for people who have some mathematical background, and it is definitely not easy going, despite the lighthearted style of the book. You really do need to do the exercises, and it helps to watch the lectures online. And I guess it wouldn’t hurt to supplement this book with an actual physics text if you plan to pursue the subject further. But as a guide to the actual mathematics of physics, this book is superb.
The book intersperses “mathematical interludes” with the physics. The interludes are short-form introductions to the necessary mathematics (derivatives, integrals, partial derivatives, etc.). By the end of the book you will be introduced to Hamiltonian mechanics and Poisson brackets - pretty advanced stuff, I think, for an introductory classical physics book!