خرید و دانلود نسخه کامل کتاب The Calculus: A Genetic Approach

TABLE OF CONTENTS……Page 16
FOREWORD……Page 6
PREFACE TO THE GERMAN EDITION……Page 12
PREFACE TO THE ENGLISH EDITION……Page 14
1. The Beginnings of Greek Speculation on Infinitesimals……Page 18
2. The Greek Theory of Proportions……Page 26
3. The Exhaustion Method of the Greeks……Page 28
4. The Modern Number Concept……Page 31
5. Archimedes’ Measurements of the Circle and the Sine Tables……Page 35
6. The Infinite Geometric Series……Page 39
7. Continuous Compound Interest……Page 41
8. Periodic Decimal Fractions……Page 45
9. Convergence and Limit……Page 50
10. Infinite Series……Page 56
11. The Quadrature of the Parabola by Archimedes……Page 60
12. Continuation after 1,880 Years……Page 69
13. Area and Definite Integral……Page 75
14. Non-rigorous Infinitesimal Methods……Page 77
15. The Concept of the Definite Integral……Page 79
16. Some Theorems on Definite Integrals……Page 86
17. Questions of Principle……Page 87
18. Tangent Problems……Page 94
20. Maxima and Minima……Page 97
21. Velocity……Page 101
22. Napier……Page 103
23. The Fundamental Theorem……Page 112
24. The Product Rule……Page 116
25. Integration by Parts……Page 120
26. Functions of Functions……Page 121
27. Transformation of Integrals……Page 122
28. The Inverse Function……Page 123
29. Trigonometric Functions……Page 130
30. Inverse Trigonometric Functions……Page 133
31. Functions of Several Functions……Page 136
32. Integration of Rational Functions……Page 138
33. Integration of Trigonometric Expressions……Page 140
34. Integration of Expressions Involving Radicals……Page 141
35. Limitations of Explicit Integration……Page 143
36. Velocity and Acceleration……Page 150
37. The Pendulum……Page 155
38. Coordinate Transformations……Page 161
39. Elastic Vibrations……Page 164
40. Kepler’s First Two Laws……Page 167
41. Derivation of Kepler’s First Two Laws from Newton’s Law……Page 173
42. Kepler’s Third Law……Page 178
EXERCISES……Page 190
Special Works on the History of the Infinitesimal Calculus……Page 200
BIBLIOGRAPHICAL NOTES……Page 202
INDEX……Page 208