数学分析与复变函数中某些初等函数性质的对比研究摘要数学分析与复变函数是数学专业两门重要基础课，但是这两者之间关系密切。我们在学习数学分析之后再学习复变函数论，是因为这二者之间存在着许多相同点与不同点。所以解决问题时，可以用已知的数学分析中的方法来解决复变函数中的问题，合理利用二者之间的关系。本题通过将定义扩展为复数，梳理一些初等函数的某些性质变化，并比较两者之间的差异和联系，以期高效学习复变函数与数学分析相关内容，深化对新旧知识的掌握，提高对数学知识的灵活运用能力，取得比较好的学习效果。关键词数学分析复变函数初等函数指数函数对数函数幂函数三角函数A Comparative Study on the Properties of Some Elementary Functions inMathematical Analysis and Complex Variable FunctionsAbstract In higher mathematics,mathematical analysis and complex variable functionsare two subjects on the surface,but the two are closely related.In university courses,westudy complex variable function theory after studying mathematical analysis,becausethese two There are many similarities and differences.So when solving problems,you canapply the methods in mathematical analysis to solve problems in complex functions,anduse the relationship between the two reasonably.As we all know,basic elementary functions can be represented by an analyticformula,then the formulas they get after compounding a finite degree must also berepresented by an analytic formula.Whether the definition is still true,and what will happen1if it is not.This topic expands to complex numbers through the number field,sorts outthe changes in the properties of some elementary functions,and compares the differencesand connections between the two.The difference between the learners,deepen the graspof old and new knowledge,improve the preparation of learning and innovation to achievebetter learning and teaching effects.Key words mathematical analysis,complex variable function,elementary function,contrast,exponential function,logarithmic function,power function,trigonometric function,periodic function目录引言1.初等函数1.1一般幂函数与一般指数函数1.2三角函数1.3对数函数2.基本性质对比…2.1极限和连续，2.2可导性、可微性.…2.3可积性2.4级数3学习复变函数的方法探讨结论…参考文献致谢…