由泰勒公式和中值定理谈一元函数微分学与多元函数微分学形式的统一

Study on the unity of single variable differential and multivariate function differential by Taylor formula and mean value theorem

利用高阶微分和方向导数,改写了多元函数的泰勒公式和拉格朗日中值定理(简称中值定理)的形式,从而将多元函数的泰勒公式和中值定理与一元函数的泰勒公式和中值定理统一起来.进一步地,可以由此出发,以一元函数微分学的视角重新认知并理解多元函数微分学.

Using the higher order differential and directional derivative,rewrite the Taylor formula and the Lagrange mean value theorem of the multivariate functions.Then,the Taylor formula and the mean value theorem of the multivariate function are unified with the Taylor formula and the mean value theorem of the single variable function.Further,it can be used to study on multivariate function differential by analogy with single variable function differential.