Analytic functions of complex variable function is the main object of study, and the five equivalent conditions of analytic functions penetrate the whole process of learning of complex function.
解析函数是复变函数论主要的研究对象，而解析函数的五个等价条件又贯穿了我们对复变函数论学习的全过程。
Line integrals are used extensively in the theory of functions of a complex variable.
在复变量函数理论中广泛使用线积分。
All of the physical quantities and basic equations of plane problem are expressed in terms of complex variable form. From the equilibrium equations, the complex stress functions are introduced.
把平面问题的物理量和基本方程全部改写为复数形式，从平衡方程出发引入了复应力函数。
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