Calculus Made Easy

Author(s)

• Silvanus P. Thompson

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)

1. Preface to the Second Edition, Prologue
2. Chapter I: To Deliver You from the Preliminary Terrors
3. Chapter II: On Different Degrees of Smallness
4. Chapter III: On Relative Growings
5. Chapter IV: Simplest Cases
6. Exercises I, Answers to Exercises I
7. Chapter V: Next Stage. What to Do With Constants
8. Exercises II, Answers to Exercises II
9. Chapter VI: Sums, Differences, Products, and Quotients
10. Exercises III, Answers to Exercises III
11. Chapter VII: Successive Differentiation
12. Exercises IV, Answers to Exercises IV
13. Chapter VIII: When Time Varies - Part 1
14. Chapter VIII: When Time Varies - Part 2
15. Exercises V, Answers to Exercises V
16. Chapter IX: Introducing a Useful Dodge
17. Exercises VI and VII, Answers to Exercises VI and VII
18. Chapter X: Geometrical Meaning of Differentiaton
19. Exercises VIII, Answers to Exercises VIII
20. Chapter XI: Maxima and Minima - Part 1
21. Chapter XI: Maxima and Minima - Part 2
22. Exercises IX, Answers to Exercises IX
23. Chapter XII: Curvature of Curves
24. Exercises X, Answers to Exercises X
25. Chapter XIII: Other Useful Dodges - Part 1: Partial Fractions
26. Exercises XI, Answers to Exercises XI
27. Chapter XIII: Other Useful Dodges - Part 2: Differential of an Inverse Function
28. Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (A)
29. Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (B)
30. Exercises XII, Answers to Exercises XII
31. Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 2: The Logarithmic Curve
32. Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 3: The Die-away Curve
33. Exercises XIII, Answers to Exercises XIII
34. Chapter XV: How to Deal With Sines and Cosines - Part 1
35. Chapter XV: How to Deal With Sines and Cosines - Part 2: Second Differential Coefficient of Sine or Cosine
36. Exercises XIV, Answers to Exercises XIV
37. Chapter XVI: Partial Differentiation - Part 1
38. Chapter XVI: Partial Differentiation - Part 2: Maxima and Minima of Functions of two Independent Variables
39. Exercises XV, Answers to Exercises XV
40. Chapter XVII: Integration - Part 1
41. Chapter XVII: Integration - Part 2: Slopes of Curves, and the Curves themselves
42. Exercises XVI, Answers to Exercises XVI
43. Chapter XVIII: Integrating as the Reverse of Differentiating - Part 1
44. Chapter XVIII: Integrating as the Reverse of Differentiating - Part 2: Integration of the Sum or Difference of two Functions
45. Chapter XVIII: Integrating as the Reverse of Differentiating - Part 3: How to Deal With Constant Terms
46. Chapter XVIII: Integrating as the Reverse of Differentiating - Part 4: Some Other Integrals
47. Chapter XVIII: Integrating as the Reverse of Differentiating - Part 5: On Double and Triple Integrals
48. Exercises XVII, Answers to Exercises XVII
49. Chapter XIX: On Finding Areas by Integrating - Part 1
50. Chapter XIX: On Finding Areas by Integrating - Part 2: Areas in Polar Coordinates
51. Chapter XIX: On Finding Areas by Integrating - Part 3: Volumes by Integration
52. Chapter XIX: On Finding Areas by Integrating - Part 4: On Quadratic Means
53. Exercises XVIII, Answers to Exercises XVIII
54. Chapter XX: Dodges, Pitfalls, and Triumphs
55. Exercises XIX, Answers to Exercises XIX
56. Chapter XXI: Finding Some Solutions - Part 1
57. Chapter XXI: Finding Some Solutions - Part 2
58. Epilogue and Apologue