What Are the Best Multivariable Calculus Books for IPhO Preparation?

[Mateus Buarque]

Hi guys, i´m pretty well in calculus 1 and i´m studying for the International Physics Olympiad. So I´d like to know some multivariable calculus books that cover vector calc too, are balanced (proofs are welcome) and emphasizes physical intuitions. Thank you already!

 

[MidgetDwarf]

Marsden and Tromba: Vector Calculus.

 

[Mateus Buarque]

Thanks, but it has pretty bad reviews on amazon, do you know why?

 

[mathwonk]

It is very hard to answer the question "why does an outstanding book that was written by great experts receive poor reviews from anonymous possibly clueless users". I read some of those to make an attempt. The best i can do is refer you to the very fair and insightful review by Jonathon DiTroia on this amazon page, written for the 5th edition (2003?):

https://www.amazon.com/dp/0716749920/?tag=pfamazon01-20

Another factor is that there are several different books by these same authors, as the book went through several revisions attempting to clarify, i.e. dumb down, a book that was originally written for Berkeley students. I taught from the 1981 edition to some strong high school students and got a range of reactions. Those students who really didn't enjoy math and were more or less forced into the course to get a star on their records hated it, while those students who went on to get PhD's in physics and math liked it fine.

In my own case I sometimes wonder why I get horrible teaching reviews in one setting and great ones in another. I did notice that I tended to get great ones primarily from honors classes and horrible ones primarily from non honors classes. Maybe that is going on in this case. I.e. this book was written for honors students at an elite school. I must say though that the most recent edition, maybe 2011 or so, looks pretty dumbed down to me. It was the only one I could review online at amazon, and even that only the first few unessential chapters. I did not myself like their treatment, but I remember it being rather better 30 years ago in the 1981 edition.

the only thing to do is for you to actually look at the book and decide for yourself whether it speaks to you or not. Maybe go to a college library and sit in the advanced calculus section until you find one on the shelf that you like. You might even like Courant, vol. 2. Another good old book with applied point of view is the early editions of Thomas, Calculus and Analytic Geometry, but not any new version. Get one back from the 1950's.

https://www.abebooks.com/servlet/Se...sortby=17&sts=t&tn=calculus&yrh=1965&yrl=1950

this covers one and several variables i think.