实数域与复数域下初等函数的异同研究  

Study on the Similarities and Differences of Elementary Functions in Real and Complex Fields

作　　者：杨立星 李玉霞 Yang Lixing;Li Yuxia(Taishan College of Science and Technology, Tai’an 271038, China)

机构地区：[1]泰山科技学院,山东泰安271038

出　　处：《黑龙江科学》2022年第11期92-94,共3页Heilongjiang Science

基　　金：山东省教育教学改革研究项目(21JG169)。

摘　　要：对实数域与复数域下初等函数的异同进行研究,通过一些例子说明了实数域与复数域下复指数函数、复三角函数、复对数函数、复幂函数这些初等函数的异同,讨论实函数与复函数的极限,将实数与微积分、复数与复变函数对应起来。复数域的函数概念可以看成是实数域函数概念的一种推广,既有很多类似之处也有不同之处,可以通过类比的方法进行学习,加深学生对复变函数概念的理解,有效降低学习难度,这样更容易掌握知识,提高学习效率。The study analyzes the similarities and differences of elementary functions in real and complex fields,and explains the similarities and differences of the elementary functions,such as exponential function,compound trigonometric function,compound log function and compound power function under real and complex fields.Function concept in complex field can be regarded as the promotion of the concept in the real field.There are some similarities and differences.It is suggested to learn through analogical method,to deepen students’understanding of complex variables functions,to make students grasp knowledge and improve learning efficiency.

关 键 词：实数域 复数域 初等函数 异同 

分 类 号：O174[理学—数学]