拉格朗日微积分的代数视角及其评价

Evaluation on Lagrange's algebraic programm of calculus

目的探讨拉格朗日微积分代数化方案的基本内涵、实质及影响。方法历史分析和文献考证。结果在拉格朗日的视野中,微积分是关于函数的一种代数形式演算,而函数是由一个解析表达式给出并且均可展成幂级数。结论拉格朗日关于微积分基础的代数化方案,虽因其函数观的局限性而最终失败,但对当时微积分学摆脱几何的束缚以及函数的抽象处理等有着决定性的影响,为19世纪基于实数系统的微积分的根本论证开辟了道路。

Aim To explore the basic connotation,essence and influence of Lagrange＇s algebraic program of calculus. Methods By historic analysis and literature study. Results In perspective of Lagrange,the calculus was a kind of algebraic calculation of the function given by an analytical expression,which could be developed into power series. Conclusion Though Lagrange＇s attempt to rebuild the foundation of algebraically is unsuccessful,it has played a decisive role on ridding the calculus of intuitive geometric notions,treating with the function in abstract,and laying a foundation for the calculus on the real number system.