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 contents 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 mathematics through some probability knowledge mainly in virtue of classical probability model and geometry probability model.At the same time two theorems about 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