Calculus Made Easy

Silvanus P. Thompson 著

58 章10h 7mEnglish1914

关于这本书

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)

章节 (57)

1Chapter I: To Deliver You from the Preliminary Terrors

156

2Chapter II: On Different Degrees of Smallness

667

3Chapter III: On Relative Growings

1046

4Chapter IV: Simplest Cases

1061

5Exercises I, Answers to Exercises I

241

6Chapter V: Next Stage. What to Do With Constants

1075

7Exercises II, Answers to Exercises II

690

8Chapter VI: Sums, Differences, Products, and Quotients

1951

9Exercises III, Answers to Exercises III

614

10Chapter VII: Successive Differentiation

329

11Exercises IV, Answers to Exercises IV

397

12Chapter VIII: When Time Varies - Part 1

973

13Chapter VIII: When Time Varies - Part 2

914

14Exercises V, Answers to Exercises V

385

15Chapter IX: Introducing a Useful Dodge

1532

16Exercises VI and VII, Answers to Exercises VI and VII

672

17Chapter X: Geometrical Meaning of Differentiaton

987

18Exercises VIII, Answers to Exercises VIII

345

19Chapter XI: Maxima and Minima - Part 1

850

20Chapter XI: Maxima and Minima - Part 2

1034

21Exercises IX, Answers to Exercises IX

343

22Chapter XII: Curvature of Curves

830

23Exercises X, Answers to Exercises X

435

24Chapter XIII: Other Useful Dodges - Part 1: Partial Fractions

1431

25Exercises XI, Answers to Exercises XI

501

26Chapter XIII: Other Useful Dodges - Part 2: Differential of an Inverse Function

323

27Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (A)

1143

28Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 1 (B)

1665

29Exercises XII, Answers to Exercises XII

416

30Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 2: The Logarithmic Curve

168

31Chapter XIV: On True Compound Interest and the Law of Organic Growth - Part 3: The Die-away Curve

1316

32Exercises XIII, Answers to Exercises XIII

495

33Chapter XV: How to Deal With Sines and Cosines - Part 1

537

34Chapter XV: How to Deal With Sines and Cosines - Part 2: Second Differential Coefficient of Sine or Cosine

397

35Exercises XIV, Answers to Exercises XIV

541

36Chapter XVI: Partial Differentiation - Part 1

456

37Chapter XVI: Partial Differentiation - Part 2: Maxima and Minima of Functions of two Independent Variables

273

38Exercises XV, Answers to Exercises XV

405

39Chapter XVII: Integration - Part 1

309

40Chapter XVII: Integration - Part 2: Slopes of Curves, and the Curves themselves

403

41Exercises XVI, Answers to Exercises XVI

130

42Chapter XVIII: Integrating as the Reverse of Differentiating - Part 1

543

43Chapter XVIII: Integrating as the Reverse of Differentiating - Part 2: Integration of the Sum or Difference of two Functions

113

44Chapter XVIII: Integrating as the Reverse of Differentiating - Part 3: How to Deal With Constant Terms

550

45Chapter XVIII: Integrating as the Reverse of Differentiating - Part 4: Some Other Integrals

359

46Chapter XVIII: Integrating as the Reverse of Differentiating - Part 5: On Double and Triple Integrals

261

47Exercises XVII, Answers to Exercises XVII

396

48Chapter XIX: On Finding Areas by Integrating - Part 1

1422

49Chapter XIX: On Finding Areas by Integrating - Part 2: Areas in Polar Coordinates

224

50Chapter XIX: On Finding Areas by Integrating - Part 3: Volumes by Integration

224

51Chapter XIX: On Finding Areas by Integrating - Part 4: On Quadratic Means

244

52Exercises XVIII, Answers to Exercises XVIII

463

53Chapter XX: Dodges, Pitfalls, and Triumphs

892

54Exercises XIX, Answers to Exercises XIX

305

55Chapter XXI: Finding Some Solutions - Part 1

900

56Chapter XXI: Finding Some Solutions - Part 2

785

57Epilogue and Apologue

205

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