Customer Reviews

Practical Analysis in One Variable

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Students of analysis are often beset with frustration. They ask "Why did you bound that quantity with that other quantity?" The typical answer, "Because it works out in the proof!" is certainly true, yet wholly unsatisfactory for the student.

This book begins with models, real-world problems, that originally motivated the development of analysis. The student easily grasps how, and more importantly why, quantities are bounded. The days of staring at an algebraic form for hours are gone! (Well, mostly.)

Instead of the normal calculus-style, simple-to-complex development of the material, Estep introduces concepts in the natural order of the real-world problems. For example, Lipschitz continuity is introduced early to solve obvious extensions to previous problems. The mathematical idea of continuity is progressively extended and provides much of the motivation for the second half of the book.

By orienting on the problems solved by analysis, Estep avoids many of the bewildering difficulties encountered in traditional introductory treatments. This is the best introductory analysis book I've seen. I'm very surprised that it hasn't received more attention.

I was amazed and pleasantly surprised when I found this book--on the shelves at my university's science and engineering library. It was one of the few math books (OK, unless you ask my wife) that I actually went and BOUGHT for my own personal library--even though it was probably going to be readily-available at the school's library. I liked it THAT much.

What surprised me wasn't only how GOOD it was, but that it took me so long to notice the book at all. In fact, though Estep's book was published in 2002, and my school acquired their copy in 2004, it seems I'm only the second person (in seven years) to borrow it. I'd never heard a reference to it (by way of comparison, for example) in the reviews of any other texts on analysis.

Now, I've looked at a LOT of (entry-level) books on (real) analysis. I think this one is a "keeper." You could probably name any book in the LC range QA299 to QA303, and I'd have *some* familiarity with it. Lang, Apostol and Rudin (Baby and Papa) of course, as well as Abbott, Strichartz (love his "Way of Analysis,"), Pugh, Thomson/Bruckner & Bruckner, you-name-it. Practical Analysis in One Variable by Estep is one I wanted on my own shelf. ALONG WITH Protter & Morrey's "First Course in Real Analysis" (get that one *instead* of Protter's "Basic Elements..."). Rosenlicht's "Intro to Analysis" (a thirteen-dollar Dover bargain) is another one I think any student of analysis won't regret buying.

Estep (a professor at Colorado State) covers all the essentials of what "real analysis" you actually SHOULD'VE learned in calculus--by re-covering functions, limits, continuity, polynomials, sequences, series, etc. in the first 15 chapters. The second section ("Differential and Integral Calculus") is 16 more chapters.

The last part (ten chapters) is titled "You Want Analysis? We've Got Your Analysis Right Here." No, really.

Nice book to develop mathematical rigor. Hardly any pre-requisites, I think, apart from high school math. Introduces concepts with motivation, which I personally found easier to follow.