The Historical Development of the Calculus

Bìa trước
Springer Science & Business Media, 6 thg 12, 2012 - 368 trang
The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.
 

Nội dung

Area Number and Limit Concepts in Antiquity
1
Incommensurable Magnitudes and Geometric Algebra
10
Area and the Method of Exhaustion
16
Volumes of Spheres
24
The Measurement of a Circle
31
The Area of an Ellipse
40
The Method of Compression
46
The Archimedean Spiral
54
28
118
The Rules of Hudde and Sluse
127
Composition of Instantaneous Motions
134
References
141
2223
164
The Arithmetic of the Infinite
166
40
184
The Calculus According to Newton
189

Solids of Revolution
62
The Method of Discovery
68
Archimedes and Calculus?
74
5
83
12
91
Early Indivisibles and Infinitesimal Techniques
95
19
111
The Calculus According to Leibniz
231
42
237
The Age of Euler
268
The Calculus According to Cauchy Riemann
301
The Twentieth Century
335
54
347
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