Regarding to Multi-Variable Calculus Books

[bacte2013]

Dear Physics Forum personnel,

I am a college sophomore with double majors in mathematics & microbiology and an aspiring analytic number theorist. I will be going to self-study the vector calculus by using Hubbard/Hubbard as a main text and Serge Lang as a supplement to Hubbard; this will help in my current self-studying of intro. analysis (Rudin's PMA, Apostol's MA, and Pugh) and also prepare me for upcoming vector calculus course (computational aspect) that I will take during the Summer. Unfortunately, my math department utilizes is own course packet for that vector calculus course, which is not that good...I am planning to purchase both Hubbard and Lang since I heard that both of them cover theories (with Hubbard using the analysis) and applications well. However, a lot of people on this forum seem to recommend Apostol Calculus II, Courant's Calculus & Analysis II, Fleming, Munkres & Spivak's manifolds, and Marsden. Are those books better than Hubbard and Serge Lang? My initial goal is to learn from Hubbard & Lang, and proceed to Spivak & Munkres's books on manifold analysis.

Please give me your advice and input! I will really appreciate them!

PK

 

[verty]

Dear Physics Forum personnel,

I am a college sophomore with double majors in mathematics & microbiology and an aspiring analytic number theorist. I will be going to self-study the vector calculus by using Hubbard/Hubbard as a main text and Serge Lang as a supplement to Hubbard; this will help in my current self-studying of intro. analysis (Rudin's PMA, Apostol's MA, and Pugh) and also prepare me for upcoming vector calculus course (computational aspect) that I will take during the Summer.

I think it will do more than prepare you. If you did work through those two books, you could perhaps manage to teach that vector calculus course.

Unfortunately, my math department utilizes is own course packet for that vector calculus course, which is not that good...I am planning to purchase both Hubbard and Lang since I heard that both of them cover theories (with Hubbard using the analysis) and applications well. However, a lot of people on this forum seem to recommend Apostol Calculus II, Courant's Calculus & Analysis II, Fleming, Munkres & Spivak's manifolds, and Marsden. Are those books better than Hubbard and Serge Lang?

I can only comment on Marsden & Tromba. It is quite calculational in the sense that a lot of the learning is through problems and repetition. It's good because of the coverage, almost every aspect has problems that test one quite thoroughly. But I wish it was more elegant because it feels sort of crude.

I agree with your choice of Lang, it seems to have good coverage and will have good problems as well. Hubbards, what can I say, I'm skeptical that a subject this difficult can be delivered in a fashion sufficiently perfect to justify the eulogism this book has received.