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.