复变函数中线性变换的几个重要结论及其应用

Some Theories and Application of Linear Transformation in Functions of Complex

线性变换是一种基本又十分重要的保形变换。对线性变换进行了一些基本研究,对线性变换给出了部分说明,在对线性变换的基本性质进行了阐述的基础上得到了几个重要结论。本文同时给出了线性变换在生产生活方面上的应用,着重介绍了保形变换在稳定温度问题上的运用,从而达到理论与实际相结合的目的。线性变换是复变函数中的一个重要内容,是一种基本又十分重要的保形变换。通过线性变换,不但可以使问题的性质更清楚,更便于分析问题,也可以使问题的求解更方便,更便于解决问题。

Linear transformation is a kind of basic and important Conformal mapping. This article do some elementary research. With instruction about Linear transformation, this thesis also explains basic characters of Linear transformation and gets several important conclusion. At the same time, it provides the application in industrial field. For example, it especially introduce the function of Conformal mapping in fixing the temperature. So it makes theory and practice together and achieves good effect. Linear transformation is the key of complex function, and also is a fundamental and significant Conformal mapping. Linear transformation, not only make problem clear and easy to be analysed,but also get more convenient way to solve the problem.