高阶微分与泰勒公式

High-order differential and Taylor formula

泰勒公式在数学分析中具有很重要的地位。由一元函数的微分出发,引出一元函数及二元函数的高阶微分,以微分形式给出一元函数及二元函数的泰勒公式,其优点是从微分到泰勒公式,形式统一。举例说明了其应用。

The Taylor formula is of important position in mathematical analysis. The definitions of the second-order differential of one or two variable function were proposed on the basis of its first-order differential of one variable function. The differential forms of the Taylor formula of one or two variable functions were also presented. Accordingly, the new form of Taylor formula is the same as that of the traditional Taylor formula, and the approximate calculation precision can then be enhanced. Some examples were given to show the salient natures.