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CONTENTS.
Chapter Page
Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
I. To deliver you from the Preliminary Terrors 1
II. On Different Degrees of Smallness . . . . . . . . . . . 3
III. On Relative Growings . . . . . . . . . . . . . . . . . . . . . . . . . . 9
IV. Simplest Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
V. Next Stage. What to do with Constants . . . . . . 25
VI. Sums, Differences, Products and Quotients . . . 34
VII. Successive Differentiation . . . . . . . . . . . . . . . . . . . . . 48
VIII. When Time Varies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
IX. Introducing a Useful Dodge . . . . . . . . . . . . . . . . . . . 66
X. Geometrical Meaning of Differentiation . . . . . . 75
XI. Maxima and Minima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
XII. Curvature of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
XIII. Other Useful Dodges . . . . . . . . . . . . . . . . . . . . . . . . . . 118
XIV. On true Compound Interest and the Law of Or？ganic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
vii
Chapter Page
XV. How to deal with Sines and Cosines . . . . . . . . . . . 162
XVI. Partial Differentiation . . . . . . . . . . . . . . . . . . . . . . . . 172
XVII. Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
XVIII. Integrating as the Reverse of Differentiating 189
XIX. On Finding Areas by Integrating . . . . . . . . . . . . . . 204
XX. Dodges, Pitfalls, and Triumphs . . . . . . . . . . . . . . . . 224
XXI. Finding some Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 232
Table of Standard Forms . . . . . . . . . . . . . . . . . . . . . . . . 249
Answers to Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
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