# Calculus Made Easy

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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.
BY
F. R. S.
SECOND EDITION, ENLARGED
MACMILLAN AND CO., LIMITED ST. MARTIN’S STREET, LONDON 1914
LONDON • BOMBAY • CALCUTTA MELBOURNE
NEW YORK • BOSTON • CHICAGO DALLAS • SAN FRANCISCO
TORONTO
COPYRIGHT.
First Edition 1910. Reprinted 1911 (twice), 1912, 1913. Second Edition 1914.
PREFACE TO THE SECOND EDITION.
The surprising success of this work has led the author to add a considerable number of worked examples and exercises. Advantage has also been taken to enlarge certain parts where experience showed that further explanations would be useful.
The author acknowledges with gratitude many valuable suggestions and letters received from teachers, students, and—critics.
October, 1914.
CONTENTS.
* CHAPTERPAGE
* Prologue................................................................................................................................................................................................................................................................................................................................................................................................xi
* I.To Deliver You From The Preliminary Terrors................................................................................................................................................................................................................................................................................................................................................................................................1
* II.On Different Degrees of Smallness................................................................................................................................................................................................................................................................................................................................................................................................3
* III.On Relative Growings................................................................................................................................................................................................................................................................................................................................................................................................9
* IV.Simplest Cases................................................................................................................................................................................................................................................................................................................................................................................................18
* V.Next Stage. What to do with Constants................................................................................................................................................................................................................................................................................................................................................................................................26
* VI.Sums, Differences, Products, and Quotients................................................................................................................................................................................................................................................................................................................................................................................................35
* VII.Successive Differentiation................................................................................................................................................................................................................................................................................................................................................................................................49
* VIII.When Time Varies................................................................................................................................................................................................................................................................................................................................................................................................52
* IX.Introducing a Useful Dodge................................................................................................................................................................................................................................................................................................................................................................................................67
* X.Geometrical Meaning of Differentiation................................................................................................................................................................................................................................................................................................................................................................................................76
* XI.Maxima and Minima................................................................................................................................................................................................................................................................................................................................................................................................93
* XII.Curvature of Curves................................................................................................................................................................................................................................................................................................................................................................................................112
* XIII.Other Useful Dodges................................................................................................................................................................................................................................................................................................................................................................................................121
* XIV.On true Compound Interest and the Law of Organic Growth................................................................................................................................................................................................................................................................................................................................................................................................134
* XV.How To Deal With Sines And Cosines................................................................................................................................................................................................................................................................................................................................................................................................165
* XVI.Partial Differentiation................................................................................................................................................................................................................................................................................................................................................................................................175
* XVII.Integration................................................................................................................................................................................................................................................................................................................................................................................................182
* XVIII.Integrating as the Reverse of Differentiating................................................................................................................................................................................................................................................................................................................................................................................................191
* XIX.On Finding Areas by Integrating................................................................................................................................................................................................................................................................................................................................................................................................206
* XX.Dodges, Pitfalls, and Triumphs................................................................................................................................................................................................................................................................................................................................................................................................226
* XXI.Finding some Solutions................................................................................................................................................................................................................................................................................................................................................................................................234
* XXII.Epilogue and Apologue................................................................................................................................................................................................................................................................................................................................................................................................249
* Table of Standard Forms................................................................................................................................................................................................................................................................................................................................................................................................252
* Answers to Exercises................................................................................................................................................................................................................................................................................................................................................................................................254
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
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