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Sadly I was off cycle at my college and I did not have a chance to take Multivariable calculus (they only offered it in the fall, and I still needed calc II). I did take Diff eq & linear algebra this last semester however. I plan to "challenge" calculus III at my college. This is where I will come in and take the final exam for the course, and whatever I score on this final will be my grade in the class. I would pay to take the class at another local college, but I honestly cannot afford to do so.

I will have to teach myself calculus III through the MIT OCW and textbooks. I have looked at several books such as courant,apostle,spivak calculus on manifolds, and stewart. Honestly the only book which I could really grasp out of these four was stewart. I get bogged down in the proof heavy approach which the other books have taken. I followed courant for a chapter and absorbed perhaps 25% of what his was talking about, however when I followed a similar chapter in stewart's book I easily absorbed most everything.

My questions are: How much will my education and chances of success suffer if I choose to learn through stewart's book? Also is there a book that lies somewhere inbetween these rigorous books and the significantly less rigorous stewart?

Any other guidance on my summer goals would be greatly appreciated.

Thanks.