Textbook recommendation for multivariate calculus?

[lalah]

I am currently studying multivariate calculus, and quite frankly, I'm not doing well. I am currently using Thomas' Calculus, 11/e media upgrade by Pearson. I don't like this book. The text is 75% theory and 25% simple examples, too few exercise problems, and the explanation is just too difficult to understand.

Can someone recommend a book that focuses less on theory, and more on the applications of multivariate calculus? To me, it's easier to learn the rote, systematic, problem-solving stuff first before understanding the theory behind it, so I want to start with that. I would also like it if it can teach how to approach solving these types of problems. It just feels like the textbook I'm currently using is, "Here's the theory. Here's one example problem. Figure out the rest yourself." I think what I want is, a book that speaks to me in "layman's terms," but not to the point where it's mathematically incorrect or unacceptable.

 

[jeffreydk]

Thomas' Calculus is a good text; a lot of applications. It'll be pretty difficult to find a book that explains calculus in layman's terms though, because there isn't really any laymans way to learn it. a really large number of extensive examples is hard to come by too--these introductory texts have to fit a lot of information and they expect that you learn how to really apply the theory through doing the problems in the manner provided by the examples.

 

[lalah]

Thomas' Calculus is a good text; a lot of applications. It'll be pretty difficult to find a book that explains calculus in layman's terms though, because there isn't really any laymans way to learn it.

For an example, there are better ways to explain how how use integration than to give me the definition, using symbols I've never seen before, and without explaining what those symbols mean. I'll read it, and not realize why they used alpha and beta instead of just plain ol' "a" and "b." Of course, that's why we have a professor, but in my case, I'm doing this as self-study.

a really large number of extensive examples is hard to come by too--these introductory texts have to fit a lot of information and they expect that you learn how to really apply the theory through doing the problems in the manner provided by the examples.

The problem is that if I have 15 problems, 8 of them are odd, I can probably figure out how to do it systematically. By that time, I would've exhausted the examples, and I really didn't learn how the theory came into play. Then the next set of exercises assume that you mastered the previous set, and go incrementally from there. But I need to learn how to solve problems where I am not told exactly what to do, just what to find.

Besides, most of the applications I see is under "Theory and Examples" in the exercise sections. I mean, besides finding volumes of arbitrarily given equations, when is it used in real life? That sort of thing.

 

[jackiefrost]

I liked Stewart's 2nd ed. - https://www.amazon.com/dp/0534378633/?tag=pfamazon01-20. Don't pay for a new one! The textbook is the second volume (Ch. 8 - 13) of a two volume set. I paid about $50 a couple years ago (used, but new cond.) and thought it was well worth it. I certainly wouldn't pay $133 for it (even if it included Vol 1, which is pretty good as well)

Overall, I think the textbook does a very decent job at presenting the material. It leans away from rigor and more toward conveying foundational concepts; hence the sub-title, "Concepts and Contexts". So, if you prefer rigor you may be disappointed.

The text has good quality computer generated color illustrations and comes with a CD with many extra teaching aids - [therefore, if you buy used, make sure it includes the CD.]. It has an adequate supply of both worked examples and problems. Answers to the odd set of problems are included in the back. There's a student solutions manual available by Dan Clagg also at Amazon.com (or wherever).

I've read many reviews of Stewart's various calculus textbooks and, as usual, they run the full spectrum from garbage to gift of the gods. I kinda like his style. Someday I would like to obtain a copy of a more rigorous multivariable calc. or vector analysis textbook just to compare the two approaches. I just haven't settled on one to gamble on yet. Maybe some version of Spivak...

jf

[edited] - I forgot something. When you get to vector calculus you may find the little booklet "Div, Grad, Curl, and all That" by Harold Shay helpful.