The Historical Development of the CalculusSpringer 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. |
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1 | |
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 |
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Thuật ngữ và cụm từ thông dụng
A₁ algebraic analytical applied Archimedes arithmetic b₁ base binomial series Cauchy century Chapter circle coefficients common logarithms computations concept continuous function convergence corresponding curve defined definition denote derivative Descartes difference differential equal equation Euler example EXERCISE Fermat Figure finite fluxions follows formula fundamental theorem geometric geometric series given gives Greek Greek mathematics height hyperbola indivisibles infinite series infinitely small infinitesimal inscribed integral interpolation interval Lebesgue Lebesgue integrable Leibniz length limit logarithms mathematics method method of exhaustion motion Napier's Newton Nlog notation obtain ordinate parabola partition polygons polynomial problems proof pyramids quadrature quantities radius ratio rational numbers real numbers rectangles result Riemann Riemann integrable rigorous segment sequence source book square subintervals substitution Table tangent line termwise tion variable vector velocity volume Wallis x₁