The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy'本课程包含下列各项主题：复数代数与函数；可解析性；轮廓积分；柯西定理；奇异性，泰勒与罗伦兹级数，留数，积分的运算；多值函数，二维的势能理论；傅立叶分析与拉普拉斯转换。