实变函数与复变函数的异同

数域从实数域扩大到复数域后,便产生了复变函数论,并且深入到了数学、微分方程、拓扑学等数学分支。复变函数论着重讨论解析函数,而解析函数的实部和虚部是相互联系的,这与实函数有根本的区别。有关实函数的一些概念,很多都可以推广到复变函数上来.例如:函数的连续性、函数的导数、有(无)界函数、中值定理、泰勒展式、基本初等函数等。

Real Variable and Complex Function of the Similarities and Differences

The complex function theory is engendered owing to that the real number domain extends to the complex domain.And the effect of the extension of number domain goes deep into the mathematic branches,such as： mathematics,differential equations,analysis situs,etc.The complex function put emphasis on studying analysis function in which its real part and false part are interrelated instead of independent.This fact marks the fundamental distinction between the analysis function and the real function.Some notions embedded in real function could be used to solve complex function questions,These notions including：the function continuity,the conception of function derivative,has（does not have） the function,theorem of mean,Taylor development,fundamental primary functions,etc.In the thesis,the author explores the differences between real function and complex function from the above-mentioned perspectives.