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I needed some guidance with calculus. I am currently a (sophomore? Sorry, I'm not following the US system) and I used stewart's book to learn single variable calculus, but I didn't do the exercises from the book, and I did the exercises at the AP level. I took my AP Calculus BC today. Although I'm hoping for a 5, I think I have the concepts but it's not entirely concrete yet.

My question is: I want to move on and learn multivariable calculus starting the end of May, probably continuing Stewart's or using Marsden. Do you think it's ok for me to do this without having a very rigorous base in single variable calculus?

And also, I know there have been many threads on this, but still, Marsden or Stewart? They both look very similar to me.

Thanks.

Edit: Oh, and to add. I am not doing all this preparation for pure math (Plan to do EE&CS). I am doing this for physics, because I enjoy physics.