定积分的发展史.docVIP

定积分的发展史 起源 定积分的概念起源于求平面图形的面积和其他一些实际问题。定积分的思想在古代数学家的工作中，就已经有了萌芽。比如古希腊时期阿基米德在公元前240年左右，就曾用求和的方法计算过抛物线弓形及其他图形的面积。公元 263 年我国刘徽提出的割圆术，也是同一思想。在历史上，积分观念的形成比微分要早。但是直到牛顿和莱布尼茨的工作出现之前（17世纪下半叶），有关定积分的种种结果还是孤立零散的，比较完整的定积分理论还未能形成，直到牛顿--莱布尼茨公式建立以后，计算问题得以解决，定积分才迅速建立发展起来。The next significant advances in integral calculus did not begin to appear until the 16th century.未来的重大进展，在微积分才开始出现，直到16世纪。 At this time the work of Cavalieri with his method of indivisibles , and work by Fermat , began to lay the foundations of modern calculus, with Cavalieri computing the integrals of x n up to degree n = 9 in Cavalieris quadrature formula .此时的卡瓦列利与他的indivisibles方法 ，并通过工作，开始卡瓦列利计算度N = 9 × N的积分奠定现代微积分的基础， 卡瓦列利的正交公式 Further steps were made in the early 17th century by Barrow and Torricelli , who provided the first hints of a connection between integration and differentiation 17世纪初Barrow provided the first proof of the fundamental theorem of calculus . Wallis generalized Cavalieris method, computing integrals of x to a general power, including negative powers and fractional powers.巴罗提供的第一个证明微积分基本定理。 At around the same time, there was also a great deal of work being done by Japanese mathematicians , particularly by Seki Kōwa . [ 3 ] He made a number of contributions, namely in methods of determining areas of figures using integrals, extending the method of exhaustion . [ edit ] Newton and Leibniz牛顿和莱布尼茨 The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz .在一体化的重大进展是在17世纪独立发现的牛顿?? 和 莱布尼茨的微积分基本定理。 The theorem demonstrates a connection between integration and differentiation.定理演示了一个整合和分化之间的连接。 This connection, combined with the comparative ease of differentiation, can be exploited to calculate integrals.这方面，分化比较容易地结合起来，可以利用来计算积分。 In particular, the fundamental theorem of calculus allows one to solve a much broader class of problems.特别是微积分基本定理，允许一个要解决的问题更广泛的类。 Equal in importance is the comprehensive math