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I always heard that engineers and physicists doing math will drive mathematicians crazy; I am an engineer myself, but doing something without fully understanding the justifications is something that always made me uncomfortable.

I tried going back to my college level calculus textbooks, but I noticed that even those have some "you can do this here, just trust us..." type explanations. To make matters worse, it seems like every website, every engineering textbook, and every math textbook use different notation and meanings for calculus things, making it hard for me to follow.

Is there any calculus textbook book that someone can recommend that they feel really gave them a really good,

*rigorous,*understanding of the material, without using shortcuts like separable variables in ODE, etc, but actually doing the math the "right" way, even if it is less intuitive?