The mathematical study of rates of change and total change, also known as “the differential and integral calculus”, has frightened generations of students. Ironically, this scholastic trauma is often unnecessary: Many formal rules of calculus are nearly trivial to carry out. The mathematical difficulties lie in understanding and using the rigorous logical framework of the calculus—what mathematicians nowadays term “elementary real analysis”—and in establishing the correctness of the formal manipulations and their connections with mathematical interpretations.
Sylvanus Phillips Thompson’s “Calculus Made Easy” gives cogent yet entertaining and irreverent explanations of these easy calculational rules. Justifications are conceptual, but beneficially simplified and intuitive. Popularized and later updated by the recreational mathematics author Martin Gardner, “Calculus Made Easy” has remained a widely-read introductory text for the past century.
With the appearance of Project Gutenberg’s public domain version on July 28, 2010, the second British edition of this classic, originally published in 1914, is freely available over the Internet. In its first weeks, the book has proved wildly popular for a mathematics text.
Thompson’s choice of material is both varied and selective. Most topics will be familiar to the modern student: Differentials as minute quantities; derivatives as relative rates of change; rules for differentiating sums, products, quotients, and compositions of functions; the geometric meaning of the first and second derivatives; finding maxima and minima; the natural exponential and logarithm functions; circular trig functions; partial derivatives; integration and antidifferentiation; the fundamental theorems; integration by parts, and by partial fractions; elementary differential equations, including exact first-order equations and d’Alembert’s solution of the one-dimensional wave equation.
If you’ve had unpleasant experiences with calculus, if your knowledge has grown rusty, or if you’ve simply never encountered this powerful and intriguing branch of mathematics, Thompson’s gem of a textbook should prove a pleasant, thought-provoking, and ultimately rewarding read.
This review was contributed by DP-volunteer adhere.
Hot off the Press 
I downloaded this book when I first saw that it had gone to PG. I have remarked to others that I wish that it had been available to me when I went through Calculus many years ago.
As remarked above the author is irreverent at times and I am intrigued by the prologue, being a fool sometimes myself:
PROLOGUE.
Considering how many fools can calculate, it is surprising that it
should be thought either a diffcult or a tedious task for any other fool
to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously diffcult.
The fools who write the textbooks of advanced mathematics|and they
are mostly clever fools|seldom take the trouble to show you how easy
the easy calculations are. On the contrary, they seem to desire to
impress you with their tremendous cleverness by going about it in the
most diffcult way.
Being myself a remarkably stupid fellow, I have had to unteach
myself the diffculties, and now beg to present to my fellow fools the
parts that are not hard. Master these thoroughly, and the rest will
follow. What one fool can do, another can.
quentin
Thank you, Andy, for another wonderful blog post! Being filled with “math anxiety” as a youngster, I never did get as far as calculus, having stopped (prudently) at trigonometry. Now that I don’t have to worry about grades, a dip into “Calculus Made Easy” seems to be in order — you’ve made it a tempting prospect.