If you have the chance, try to go through a formal proof and analysis based course that requires convergence proofs and all that (mathematical "analysis" isn't what you might think; it's a specific subject). For calculus, it is what drove home the point and the magic for me.

We used this book (https://smile.amazon.com/Introduction-Calculus-Analysis-Clas...) but I expect it may be a bad fit for self study. Try to find something with similar subject matter.