复变函数可导充要条件证明的另一种方法及应用

Another method and application of sufficient and necessary condition proof for complex variable functions

复变函数基本理论的在流体力学、计算机科学、信号系统等领域有广泛的应用,深入了解复变函数性质,更容易分析曲线伸缩率、信号系统处理与分析及解决微分方程的初值等问题,判断复变函数是否可导,能够为解决实际问题提供决策指导和理论依据.提出复变函数可导充要条件的证明方法,通过假设复变函数可导,利用复变函数求导的定义法证明复变函数实部与虚部满足在某点可微且满足C-R方程即可导的必要条件;另一方面,利用满足C-R方程和可微的条件,判断复变函数可导,即给出了可导的充分条件,最后利用算例对该证明方法进行了验证,证明该方法能更快且有效地判断复变函数可导性.

The basic theory of complex function in fluid mechanics,computer science,signal system and other fields had a wide range of applications,further understand the properties of complex function,it was easier to analyze curve slip rate,signal processing and analysis system and solved the initial value problems of differential equation,determining whether a complex function could provide decision-making guidance and theoretical basis for practical problem solving.In this paper,a method to prove the necessary and sufficient conditions for the derivation of a complex function was proposed,by assuming the derivation of a complex function,the necessary conditions for the derivation of the real and imaginary parts of a complex function were proved by using the definition method of the derivation of a complex function.On the other hand,by using the conditions satisfying C-R equation and differentiability,the derivability of complex function was judged,that the sufficient conditions for the derivability were given.Finally,an example was used to verify the proof method,which proved that the method could judge the derivability of complex function more quickly and effectively.