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)
Rozdziały (57)
1Chapter I: To Deliver You from the Preliminary Terrors
2:36
2Chapter II: On Different Degrees of Smallness
11:07
3Chapter III: On Relative Growings
17:26
4Chapter IV: Simplest Cases
17:41
5Exercises I, Answers to Exercises I
4:01
6Chapter V: Next Stage. What to Do With Constants
17:55
7Exercises II, Answers to Exercises II
11:30
8Chapter VI: Sums, Differences, Products, and Quotients
32:31
9Exercises III, Answers to Exercises III
10:14
10Chapter VII: Successive Differentiation
5:29
11Exercises IV, Answers to Exercises IV
6:37
12Chapter VIII: When Time Varies - Part 1
16:13
13Chapter VIII: When Time Varies - Part 2
15:14
14Exercises V, Answers to Exercises V
6:25
15Chapter IX: Introducing a Useful Dodge
25:32
16Exercises VI and VII, Answers to Exercises VI and VII
11:12
17Chapter X: Geometrical Meaning of Differentiaton
16:27
18Exercises VIII, Answers to Exercises VIII
5:45
19Chapter XI: Maxima and Minima - Part 1
14:10
20Chapter XI: Maxima and Minima - Part 2
17:14
21Exercises IX, Answers to Exercises IX
5:43
22Chapter XII: Curvature of Curves
13:50
23Exercises X, Answers to Exercises X
7:15
24Chapter XIII: Other Useful Dodges - Part 1: Partial Fractions
23:51
25Exercises XI, Answers to Exercises XI
8:21
26Chapter XIII: Other Useful Dodges - Part 2: Differential of an Inverse Function
5:23
27Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (A)
19:03
28Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (B)
27:45
29Exercises XII, Answers to Exercises XII
6:56
30Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 2: The Logarithmic Curve
2:48
31Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 3: The Die-away Curve
21:56
32Exercises XIII, Answers to Exercises XIII
8:15
33Chapter XV: How to Deal With Sines and Cosines - Part 1
8:57
34Chapter XV: How to Deal With Sines and Cosines - Part 2: Second Differential Coefficient of Sine or Cosine
6:37
35Exercises XIV, Answers to Exercises XIV
9:01
36Chapter XVI: Partial Differentiation - Part 1
7:36
37Chapter XVI: Partial Differentiation - Part 2: Maxima and Minima of Functions of two Independent Variables
4:33
38Exercises XV, Answers to Exercises XV
6:45
39Chapter XVII: Integration - Part 1
5:09
40Chapter XVII: Integration - Part 2: Slopes of Curves, and the Curves themselves
6:43
41Exercises XVI, Answers to Exercises XVI
2:10
42Chapter XVIII: Integrating as the Reverse of Differentiating - Part 1
9:03
43Chapter XVIII: Integrating as the Reverse of Differentiating - Part 2: Integration of the Sum or Difference of two Functions
1:53
44Chapter XVIII: Integrating as the Reverse of Differentiating - Part 3: How to Deal With Constant Terms
9:10
45Chapter XVIII: Integrating as the Reverse of Differentiating - Part 4: Some Other Integrals
5:59
46Chapter XVIII: Integrating as the Reverse of Differentiating - Part 5: On Double and Triple Integrals
4:21
47Exercises XVII, Answers to Exercises XVII
6:36
48Chapter XIX: On Finding Areas by Integrating - Part 1
23:42
49Chapter XIX: On Finding Areas by Integrating - Part 2: Areas in Polar Coordinates
3:44
50Chapter XIX: On Finding Areas by Integrating - Part 3: Volumes by Integration
3:44
51Chapter XIX: On Finding Areas by Integrating - Part 4: On Quadratic Means
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