differential calculus integral calculus€¦ · some calculus-tricks are quite easy. some a!"e...
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Calculus Made EasyDifferential Calculus
&
Integral Calculus
by
Silvanus P. Thompson(1943)
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ISBN: 978-1-62992-028-3
Published by Fairhaven Press
Cover design and protectable materials are copyright (2018) by Fairhaven Press Inc. All rights reserved. No part of this publication may be copied, scanned, photographed, stored in a retrieval system, posted online, or transmitted by any means, electronic, mechanical, recording or otherwise, except brief extracts for the purpose of review, and no part of this publication may be sold or hired, without the express written permission of the publisher. The front and back covers also contained trademarked elements which also apply to these restrictions.
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www.fairhavenpress.com
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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
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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
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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.
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