What Makes Apostol's Advanced Calculus Text Stand Out?

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im looking for an advanced calculus text somthing with more difficult problems than stewart. not an analytical style text but somthing with a good number of exercises covering topics in integral and differential calculus.
 
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Tom M. Apostol's two-volume book is "the other" classic besides Spivak. It's rigorous, but it's a rigorous calculus text, not a "baby real analysis" book like Spivak. It covers single-variable calculus, basic differential equations, elementary linear algebra, multivariable calculus, and the beginnings of probability theory. There are a large number of exercises, both computational and theoretical. Some of them are challenging.

Small points against this book are that Apostol's writing is somewhat dry and boring and that he covers integration before differentiation, which some people find strange. It's also quite expensive, but it's old and has been a standard text for many years, so your library is likely to have a copy.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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