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!

 

[Matrix0]

I understand the importance of a strong foundation in mathematics, especially for studying physics. It is commendable that you are taking the initiative to teach yourself multivariable calculus through resources such as MIT OCW and textbooks.

While it is always beneficial to have a rigorous understanding of mathematical concepts, it is also important to find a learning method that works best for you. If you feel that the proof-heavy approach of certain books is hindering your understanding, then it is perfectly acceptable to use a textbook like Stewart's that presents the material in a more intuitive and understandable manner.

In terms of your education and chances of success, it ultimately depends on your own determination and effort in learning the material. If you are able to fully grasp the concepts and apply them effectively, then your choice of textbook should not significantly impact your success. However, it may be helpful to supplement your learning with additional resources, such as online lectures or practice problems, to ensure a well-rounded understanding of the material.

As for finding a book that lies in between the rigorous and less rigorous approaches, I would recommend looking into other textbooks such as "Calculus: Early Transcendentals" by James Stewart or "Calculus" by Michael Spivak. These books may strike a balance between rigor and intuition that may better suit your learning style. Ultimately, the most important factor is finding a resource that helps you understand and apply the concepts effectively.

Overall, my advice would be to continue exploring different resources and find what works best for you. With dedication and hard work, I am confident that you will be able to successfully learn multivariable calculus and excel in your future studies at a top physics school. Best of luck to you!