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I'm looking for a text that covers roughly what's sometimes called "Calculus III" or multivariable calculus.* But this text must satisfy certain additional criteria: (1) It must be more in-depth (and consequently have harder exercises) than usual; (2) It must contain many solutions to the exercises; (3) It must not engage in the sort of unconvincing hand-waving common to "mathematical methods" texts.

Basically I'm looking for a difficult, thorough version of a calc 3 text. Bonus points if the book discusses differentials.

PS: I'm aware that a somewhat similar question has been asked here

Multivariable calculus: hard problems with solutions

but the problems in the books recommended were not hard enough.

*The sort of material in Stewart's Calculus.

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Jacob Turley
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  • I'm not sure exactly what is in "Calc III" but if the problems in Schuam's outlines are too easy and you want to learn about differentials, then you can safely move on from "Multivariable calculus" to Calculus/Analysis on manifolds. Munkre's has a great book in this area, it is a relatively gentle introduction. Spivak's "Calculus on Manifolds" is also nice though its thinness is both a positive and negative feature. – Ragib Zaman Sep 09 '13 at 08:29
  • I just googled Munkre's book for nostalgic purposes and came across this review and comparison of Munkres and Spivak's texts. Mathwonk is a knowledgeable professor so there is some weight in his opinion. No one is forcing you to do exercises that you find too easy so I still prefer Munkres. – Ragib Zaman Sep 09 '13 at 08:36
  • Try looking at this book (in most every college and university library): Introduction to Calculus and Analysis, Volume 2 by Richard Courant and Fritz John. Although the later parts of the book are quite advanced, the book does not assume any previous knowledge of multivariable calculus. – Dave L. Renfro Sep 11 '13 at 20:17
  • @DaveL.Renfro It looks good. Where are the solutions to the exercises? – newb Sep 30 '13 at 12:24
  • @newb: Volume 2 of Courant/John has a lengthy solutions section at the end of the book -- over 100 pages, on pp. 821-939. – Dave L. Renfro Sep 30 '13 at 17:30
  • @DaveL.Renfro That's awesome, thanks for the recommendation! (It didn't show for me on Amazon) – newb Oct 01 '13 at 12:15
  • @newb: There seems to be a freely available copy of volume 2 on the internet (may not be legal, I don't know). Google the phrase "Introduction to Calculus and Analysis" with the word "carlossicoli". – Dave L. Renfro Oct 01 '13 at 15:14

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