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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 is is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject. (from Wikipedia)

Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks 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. (from the Prologue)

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Calculus Made Easy

Chapters

Preface to the Second Edition, Prologue

Chapter I: To Deliver You from the Preliminary Terrors

Chapter II: On Different Degrees of Smallness

Chapter III: On Relative Growings

Chapter IV: Simplest Cases

Exercises I, Answers to Exercises I

Chapter V: Next Stage. What to Do With Constants

Exercises II, Answers to Exercises II

Chapter VI: Sums, Differences, Products, and Quotients

Exercises III, Answers to Exercises III

Chapter VII: Successive Differentiation

Exercises IV, Answers to Exercises IV

Chapter VIII: When Time Varies - Part 1

Chapter VIII: When Time Varies - Part 2

Exercises V, Answers to Exercises V

Chapter IX: Introducing a Useful Dodge

Exercises VI and VII, Answers to Exercises VI and VII

Chapter X: Geometrical Meaning of Differentiaton

Exercises VIII, Answers to Exercises VIII

Chapter XI: Maxima and Minima - Part 1

Chapter XI: Maxima and Minima - Part 2

Exercises IX, Answers to Exercises IX

Chapter XII: Curvature of Curves

Exercises X, Answers to Exercises X

Chapter XIII: Other Useful Dodges - Part 1: Partial Fractions

Exercises XI, Answers to Exercises XI

Chapter XIII: Other Useful Dodges - Part 2: Differential of an Inverse Function

Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (A)

Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (B)

Exercises XII, Answers to Exercises XII

Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 2: The Logarithmic Curve

Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 3: The Die-away Curve

Exercises XIII, Answers to Exercises XIII

Chapter XV: How to Deal With Sines and Cosines - Part 1

Chapter XV: How to Deal With Sines and Cosines - Part 2: Second Differential Coefficient of Sine or Cosine

Exercises XIV, Answers to Exercises XIV

Chapter XVI: Partial Differentiation - Part 1

Chapter XVI: Partial Differentiation - Part 2: Maxima and Minima of Functions of two Independent Variables

Exercises XV, Answers to Exercises XV

Chapter XVII: Integration - Part 1

Chapter XVII: Integration - Part 2: Slopes of Curves, and the Curves themselves

Exercises XVI, Answers to Exercises XVI

Chapter XVIII: Integrating as the Reverse of Differentiating - Part 1

Chapter XVIII: Integrating as the Reverse of Differentiating - Part 2: Integration of the Sum or Difference of two Functions

Chapter XVIII: Integrating as the Reverse of Differentiating - Part 3: How to Deal With Constant Terms

Chapter XVIII: Integrating as the Reverse of Differentiating - Part 4: Some Other Integrals

Chapter XVIII: Integrating as the Reverse of Differentiating - Part 5: On Double and Triple Integrals

Exercises XVII, Answers to Exercises XVII

Chapter XIX: On Finding Areas by Integrating - Part 1

Chapter XIX: On Finding Areas by Integrating - Part 2: Areas in Polar Coordinates

Chapter XIX: On Finding Areas by Integrating - Part 3: Volumes by Integration

Chapter XIX: On Finding Areas by Integrating - Part 4: On Quadratic Means

Exercises XVIII, Answers to Exercises XVIII

Chapter XX: Dodges, Pitfalls, and Triumphs

Exercises XIX, Answers to Exercises XIX

Chapter XXI: Finding Some Solutions - Part 1

Chapter XXI: Finding Some Solutions - Part 2

Epilogue and Apologue