Calculus and Its Origins (Spectrum) 1st edition by Perkins, David (2012) Hardcover

Spectrum

by David Perkins

Calculus answers questions that had been explored for centuries before calculus was born. Calculus and Its Origins begins with these ancient questions and details the remarkable story of how subsequent scholars wove these inquiries into a unified theory. This book does not presuppose knowledge of calculus, it requires only a basic knowledge of geometry and algebra (similar triangles, polynomials, factoring). Inside you will find the accounts of how Archimedes discovered the area of a parabolic segment, ibn Al-Haytham calculated the volume of a revolved area, Jyesthadeva explained the infinite series for sine and cosine, Wallis deduced the link between hyperbolas and logarithms, Newton generalized the binomial theorem, Leibniz discovered integration by parts, and much more. Each chapter ends with further results, in the form of exercises, by such luminaries as Pascal, Maclaurin, Barrow, Cauchy and Euler.

Genres: Mathematics

Hardcover

First published June 1, 2012

Reviews

[Charles · Rating 5 out of 5]

Differential and integral calculus is a subject that you can learn in a few courses, but it often takes many more years before it is truly appreciated. The enormous breadth of subjects where it is used can astound even veterans of the practice of the art, recently I was tutoring a student in AP calculus and we were discussing the derivative as a rate of change. I told her that since all things in the world change over time, the derivative describes everything. It may have been a bit of hyperbole, but at most only a bit.
This book traces the mathematical and historical roots of calculus and it quite rightly begins with a couple of forms of Zeno's paradox. As is nearly always the case something is labeled as a paradox when it is not completely understood and that is the case with Zeno's famous puzzle. The fundamentals of limits and calculus explain the solution to Zeno's paradox quite well, but it took centuries of incremental advancement and the work of several geniuses to get there.
That work is summarized in a very succinct and effective manner by Perkins; he walks through the major discoveries that moved the level of understanding progressively upward. The explanations are very well done, with suitable instructor help; they can be understood by anyone that has gone through the complete high school course sequence in algebra and geometry.
This book could also be used in a course in the history of mathematics; exercises that take the students in directions that extend the material are included at the end of the chapters. Solutions are not included because they are to be in essay form and generally require some research. They are very good and are challenging enough so that any subset could serve as the basis of a complete grade.
No matter what level of mathematics you reach or area you work in, there are books that will always be worthy of reading. This is one of them.

Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon

[Nicole · Rating 4 out of 5]

As a math book it is an easy and fun read. And then you beat you beat your head against the mathematics contained within its pages.