Need some guidance in learning multivar calculus

[ozone]

Next semester I am transferring out of my community college to a top 50 physics school in the U.S.

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.

 

[micromass]

Do you know what textbook they use in the college course?? If they follow Stewart, then there is no real reason to study a rigorous book like Spivak.

In any case, there is no problem at all in studying from Stewart first. Stewart is an easier and more applied book than the other texts, and this is good because you can use it to build intuition.
After you did Stewart, you can take a more rigorous book and study from that. You will then find the rigorous book much easier to understand because you already have the required intuition.
You could also study Stewart and a rigorous book at the same time.

Some other books you might be interested in are:
https://www.amazon.com/dp/0130414085/?tag=pfamazon01-20

and

https://www.amazon.com/dp/0486683362/?tag=pfamazon01-20

These are two excellent books. They are quite rigorous, but easier than the books you mentioned. Check them out to see what you think of them!

 

[ozone]

I read on their syllabus that they follow transcendental calculus by Stewart, but the PDF I have been viewing is just calculus by stewart (I have been looking at pdf's before I commit to purchasing a book). So I am not entirely sure if they are the same book but I imagine they are similar enough.

I will try and take a peak at the two you suggested to see if they are more valuable.

Thanks for the advice.

 

[micromass]

If they follow a Stewart-like book, then I think that studying Stewart should be sufficient for your goals!