### Calculus book

#### 2013-04-30 02:12:33

(Warning: technical!)

Not long ago, in the IU Southeast library, I noticed an old calculus book, a rather unusual book. It was a fairly slender book, and a glance at its contents showed several unusual things about the book: It was intended as an introductory calculus text, yet had a rather theoretical focus that was closer to an introductory analysis text (a course about the theory underpinning calculus, commonly taught at the junior or senior level). I also noticed that it covered integration before differentiation, unlike any other calculus text I've ever seen, and it also had a calculation of the integral of the sine function from the definition of integral in terms of limits of Riemann sums (using a deft bit of trig to sum the Riemann sum in closed form). These features grabbed my attention because these describe a calculus book I found in my high school library when I was 16 and began teaching myself calculus. I have always wanted to find out what book that was, because it brings to mind the wonderful feeling of discovery when I began to understand the calculus. I'm almost certain the book I found our library at IU Southeast is the same book. It turns out the book is *Calculus, An Introductory Approach*, by Ivan Niven. I ordered a used copy through Amazon, which arrived today. The copy I have is the second edition, published in 1966 by D. Van Nostrand (the first edition appeared in 1961). This would have made the book 10--15 years old when I saw it as a 16-year-old.

The author, by the way, was a professor at the University of Oregon, and he was in his final year there in my first year in graduate school at Oregon. I was very impressed by him; he gave lucid talks in number theory (his mathematical specialty). One thing he is known for finding a simple proof using elementary calculus that the number pi is irrational. (Ivan Niven died at about age 84 in 1999; the Wikipedia has an article about him.)