《复变函数与积分变换2》课程教学大纲.docxVIP

《复变函数与积分变换2》教学大纲 一、课程基本信息 课程名称 复变函数与积分变换 Complex Function and Integral Transformation 课程编码 SCC210611030 开课院部 理学院 课程团队 （未设置） 学分 3.0 课内学时 48 讲授 48 实验 0 上机 0 实践 0 课外学时 0 适用专业 电子信息工程 授课语言 中文 先修课程 高等数学（2-1）、高等数学（2-2） 课程简介 （必修） 本课程是由复变函数（也称复分析）和积分变换两部分构成，是高等数学的后续课程。复变函数是一个古老而又重要的数学分支，它内容丰富，在科学和工程技术中有着非常广泛的应用，是解决诸如流体力学、热学、电磁学和平面弹性力学的有力工具。复变函数的主要内容包括复数及其运算，复变函数的基本概念，解析函数及性质，复变函数的积分，复数级数及解析函数的级数表示，留数理论及其应用等。积分变换包括傅立叶变换和拉普拉斯变换。积分变换是解决频谱分析、信号分析、线性系统分析、微分方程求解等问题的重要工具，在电气工程、通信与控制、图像处理、机械系统、流体力学、地质勘探与地震预报等许多工程技术领域均有广泛应用。通过《复变函数与积分变换》课程的学习，不仅可以掌握复变函数与积分变换的基础理论及数学方法，还将为后续有关课程的学习奠定必要的数学基础，提高学生利用数学知识解决实际工程和技术中相关问题的能力。 This course includes two part contents which are complex variable function and integral transformation. Complex variable function theory is an ancient and important branch of mathematics. It is rich in content and has important role in natural science and engineering technology researching. It is also a powerful tool to solve the problems, such as fluid mechanics, thermodynamics, electromagnetics, and the plane elasticity and so on. The contents of complex variable function mainly includes the plural and its operation, the basic concept of complex variable function，the analytic function and its related properties, complex variable function integral, Complex series and series representations of analytic functions, residue theory and its application, etc. Integral transformation includes Fourier transformation and Laplace transformation. It is an important tool for spectrum analysis, signal analysis, linear system analysis, and differential equation solving. Integral transformation has been widely used in many engineering fields, such as electrical engineering, communication and control, image processing, mechanical system, fluid mechanics, geological exploration and earthquake prediction. By learning the course 《complex function and integral transformation》，students can not only master the basic theory and method of the mathematics curriculum, but also will lay the neces