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I'm studying Stewart's multivariable calculus book and I find most the examples and exercises pretty easy and repetitive. I would like to know if there are books in multivariable calculus with more intriguing and interesting examples. Just to make a comparison with one-variable calculus, I find Spivak's calculus book more interesting with less repetitive exercises than standard books.

Remark: Just to be clear, I'm requesting for a book which doesn't necessarily need to be more theoretical, just having more interesting examples.

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  • $\begingroup$ I've had Vector Calculus by Peter Baxandall and Hans Liebeck recommended to me multiple times. I haven't had the time to check it out myself yet, but it may be woth looking at. $\endgroup$
    – Mitchell Faas
    Commented Apr 17, 2017 at 12:40
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    $\begingroup$ I know you're not talking about rigour specifically, but it's impossible to say anything meaningful about Spivak's book if you don't first mention that it's more theoretical and at a much higher level of difficulty than, say, Stewart. The examples in Spivak would mostly not be accessible to you if you weren't prepared to operate at that level of rigour. A similar book, but for multivariable calculus, would be Apostol's Calculus, Vol. 2. A book intermediate in rigour between Stewart and Apostol might be Lang's Calculus of Several Variables. $\endgroup$
    – user49640
    Commented Apr 17, 2017 at 21:09

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Try the extended exercises in Jon Rogawski's Calculus Text. What you can also do is a find a very elementary physics with calculus text. Most non-theoretical calculus text will have problems that seem repetitive because the point is to get you to the level of being able to solve those problems without much thinking. In the world of an engineer, physicts, etc, time is extremely important, so this approach is almost optimal.

There is almost no middle ground for non-theoretical and very rigorous calculus texts. In my opinion, you either do it one way or the other, the choice of presentation depending on the audience. One may disagree with this, but how I see it, a realtor only needs to know general things about a house, not how to actually build it. The physics + calculus is a good option because there you'll build a more intuitive understanding about the mathematics in multivariable calculus, since basically this was the math built to solve those types of problems.

Opinions on what I wrote above will vary greatly. I am not saying this is the best approach, but if you want to get a better understanding of why I suggested the above, read this article V.Arnold, "On Teaching Mathematics".

Be warned! There is an extreme bias in this article due to the culture of mathematics that Arnold came from.

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  • $\begingroup$ Why an elementary physics book with calculus text? Are their exercises/examples better than the standard books of calculus? $\endgroup$
    – user42912
    Commented Apr 18, 2017 at 6:50
  • $\begingroup$ Read the above. I suggested the physics text because multivariable mathematics solves undergraduate physics problems. $\endgroup$
    – Faraad Armwood
    Commented Apr 18, 2017 at 22:30

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