高等数学在中学数学恒等式证明中的应用

高等数学在中学数学恒等式证明中的应用

摘要

概率论、导数、复数、牛顿插值法、齐次多项式是高等数学中的知识，本文用概率论中的古典概型、几何概型等概率论知识证明了组合恒等式、自然恒等式等高中数学中的1系列恒等式，而且提出并证明了与复数、牛顿插值法、齐次多项式有关的两个定理，并运用它们和导数证明了高中数学中的恒等式．

关键词：概率模型；导数；复数；牛顿插值法

The Applications of Higher Mathematics for the Demonstration of Identical Equation in the High-school Mathematics

☢ABSTRACT

The contฏents about probability,derivative,complex number,Newton inserting method,homogeneous polynomial are studied in higher mathematics.This article demonstrates a series of identical equations such as combination identical equation, natural identical equation,which appears frequently in high-school ヅmathematics through some probability knowledge mainly in virtue of classical probability model and geometry probability model.At the same time two theorems abou♀t complex number、Newton interpolation method and homogeneous polynomial are proved and some identical equation in the high-school mathematics are also demonstrated through the two theorems and the theory of derivative.

Key words: probability model;derivative;complex number;Newton inserting method❧