I've been going through the AOPS Calculus textbook, and I genuinely really enjoy reading this textbook. I enjoy the format, where if I had to break it down:
1 - Introduce a problem, or a goal, basically give something that the section of the book is working towards (for example, when talking about limits towards/involving infinity, presenting the need to more generally be able to rigorously take the limits of quotients of functions)
2 - Begin working to the solution, developing "suboptimal" or incomplete methods (for example, taking the limits of quotients of rational functions going to infinity by dividing both functions by some power of x)
3 - Work towards a more general solution, with a good amount of rigour and providing good intuition but without getting too lost in the weeds (introducing the reader to use tangent line approximations to try to approximate the limit, then showing how the error of the approximation of f cancels with that of g, but leaving some of the more complex proofs involving the generalization of L'Hopital's rule to a special section)
4 - Have creative, hard, clever, and interesting exercises to drive the learned material home
I really enjoy this format, I feel as though I have a good amount of rigor here, a strong ability to prove the things that I use when solving, good intuition for what I'm doing, and I'm really having fun solving these creative difficult problems. I'm looking for books that achieve all/most of the above well, while not losing the intuition/beauty of the mathematics in the weeds of the specific proofs (I like rigor, but I think it would be best if someone of the more complex proofs, (to give an example from calc, the proof for IVT) were left to their own section/subsection or an exercise). I would like to do something that leverages calculus in some way, but something which does not is also fine. I've been looking into Hubbard & Hubbard Vector Calc and Linalg, as well as Strogatz Nonlinear Dynamics and Chaos. Thoughts or recommendations?