Gardner Martin - Calculus made easy: being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus

Fads and Fallacies in the Name of Science

Mathematics, Magic, and Mystery

Great Essays in Science (ed.)

Logic Machines and Diagrams

The Scientific American Book of Mathematical Puzzles and Diversions

The Annotated Alice

The Second Scientific American Book of Mathematical Puzzles and Diversions

Relativity for the Million

The Annotated Snark

The Ambidextrous Universe

The Annotated Ancient Mariner

New Mathematical Diversions from Scientific American

The Annotated Casey at the Bat

Perplexing Puzzles and Tantalizing Teasers

The Unexpected Hanging and Other Mathematical Diversions

Never Make Fun of a Turtle, My Son (verse)

The Sixth Book of Mathematical Games from Scientific American

Codes, Ciphers, and Secret Writing

Space Puzzles

The Snark Puzzle Book

The Flight of Peter Fromm (novel)

Mathematical Magic Show

More Perplexing Puzzles and Tantalizing Teasers

The Encyclopedia of Impromptu Magic

Aha! Insight

Mathematical Carnival

Science: Good, Bad, and Bogus

Science Fiction Puzzle Tales

Aha! Gotcha

Wheels, Life, and Other Mathematical Amusements

Order and Surprise

The Whys of a Philosophical Scrivener

Puzzles from Other Worlds

The Magic Numbers of Dr. Matrix

Knotted Doughnuts and Other Mathematical Entertainments

The Wreck of the Titanic Foretold

Riddles of the Sphinx

The Annotated Innocence of Father Brown

The No-Sided Professor (short stories)

Time Travel and Other Mathematical Bewilderments

The New Age: Notes of a Fringe Watcher

Gardners Whys and Wherefores

Penrose Tiles to Trapdoor Ciphers

How Not to Test a Psychic

The New Ambidextrous Universe

More Annotated Alice

The Annotated Night Before Christmas

Best Remembered Poems (ed.)

Fractal Music, Hypercards, and More

The Healing Revelations of Mary Baker Eddy

Martin Gardner Presents

My Best Mathematical and Logic Puzzles

Classic Brainteasers

Famous Poems of Bygone Days (ed.)

Urantia: The Great Cult Mystery

The Universe Inside a Handkerchief

The Night Is Large

Last Recreations

Visitors from Oz

BEING A VERY-SIMPLEST INTRODUCTION TO THOSE
BEAUTIFUL METHODS OF RECKONING WHICH
ARE GENERALLY CALLED BY THE
TERRIFYING NAMES
OF THE

DIFFERENTIAL CALCULUS
AND THE
INTEGRAL CALCULUS

Newly Revised, Updated, Expanded, and
Annotated for its 1998 edition.

The author and publisher have provided this e-book to you for your personal use only. You may not make this e-book publicly available in any way. Copyright infringement is against the law. If you believe the copy of this e-book you are reading infringes on the authors copyright, please notify the publisher at: us.macmillanusa.com/piracy.

CALCULUS MADE EASY . Copyright 1998 by Martin Gardner. All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles or reviews. For information, address St. Martins Press, 175 Fifth Avenue, New York, N.Y. 10010.

The original edition of Calculus Made Easy was written by Silvanus P. Thompson and published in 1910, with subsequent editions in 1914 and 1946.

Production Editor: David Stanford Burr
Design: Susan Hood

Library of Congress CataloginginPublication Data

Thompson, Silvanus Phillips, 18511916.

Calculus made easy : being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus. Newly rev., updated, expanded, and annotated for its 1998 ed. / Silvanus P. Thompson and Martin Gardner.

p. cm.

ISBN 0-312-18548-0
eISBN 978-1-4668-6635-5

1. Calculus. I. Gardner, Martin. II. Title.

QA303.T45 1998

515dc21

98-10433
CIP

Introductory courses in calculus are now routinely taught to high school students and college freshmen. For students who hope to become mathematicians or to enter professions that require a knowledge of calculus, such courses are the highest hurdle they have to jump. Studies show that almost half of college freshmen who take a course in calculus fail to pass. Those who fail almost always abandon plans to major in mathematics, physics, or engineeringthree fields where advanced calculus is essential. They may even decide against entering such professions as architecture, the behavioral sciences, or the social sciences (especially economics) where calculus can be useful. They exit what they fear will be too difficult a road to consider careers where entrance roads are easier.

One reason for such a high dropout rate is that introductory calculus is so poorly taught. Classes tend to be so boring that students sometimes fall asleep. Calculus textbooks get fatter and fatter every year, with more multicolor overlays, computer graphics, and photographs of eminent mathematicians (starting with Newton and Leibniz), yet they never seem easier to comprehend. You look through them in vain for simple, clear exposition and for problems that will hook a students interest. Their exercises have, as one mathematician recently put it, the dignity of solving crossword puzzles. Modern calculus textbooks often contain more than a thousand pagesheavy enough to make excellent doorstopsand more than a thousand frightening exercises! Their prices are rapidly approaching $100.

Why do calculus books weigh so much? Lynn Arthur Steen asked in a paper on Twenty Questions for Calculus Reformers that is reprinted in Toward a Lean and Lively Calculus (Mathematical Association of America, 1986), edited by Ronald Douglas. Because, he answers, the economics of publishing compels authors to add every topic that anyone might want so that no one can reject the book just because some particular item is omitted. The result is an encyclopaedic compendium of techniques, examples, exercises and problems that more resemble an overgrown workbook than an intellectually stimulating introduction to a magnificent subject.

The teaching of calculus is a national disgrace, Steen, a mathematician at St. Olaf College, later declared. Too often calculus is taught by inexperienced instructors to ill-prepared students in an environment with insufficient feedback.