Calculus Made EasyDifferential Calculus

&

Integral Calculus

by

Silvanus P. Thompson(1943)

ISBN: 978-1-62992-028-3

Published by Fairhaven Press

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CONTENTS.

f'JBA.PTER. P.t.OII

PROLOGUE·

J. To DELIVER YOU FROM THE PRELIMINARY TER-

MM · 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

VJ. SUMS, DIFFERENCES, PRODUCTS, AND QUOTIENTS 35

VII. SUCCESSIVE DIFFERENTIATION

VIII. WHEN TIME VARIES -

IX. INTRODUCING A USEFUL DODGE

49

52

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 CosINI!S •

XVI. p ARTIAL DIFFERENTIATION

XVII. INTEGRATION

• 165

• 175

• 182

x CONTENTS

XVIII. INTEGRATING AS THE REV.ERSE OF DIFFERENTIATING 191

XIX. ON FINDING AREAS BY INTEGRATING

:XX. DODGES, PITFALLS, AND TRIUMPHS

XXI. FINDING SOME SOLUTIONS •

• 206

• 226

• 234

:XXJJ. .A_ LITTLE MORE ABOUT CURVATURE OF CURVES • 9.49

XXIII. How TO FIND THE LENGTH OF AN .A.Re ON .._ CuRVE • • 26(1

EPILOGUE AND APOLOGUE •

Table of Standard Forms

ANSWERS TO EXERCISES

• 283

• 286

· 288

PROLOGUE.

CoNSIDERING how many fools can calculate, it is

surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the �ame tricks.

Some calculus-tricks are quite easy. Some a!"e enormously difficult. The fools who write the text- . books 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 difficult way.

Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, 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.