1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请
联系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
复变函数 Complex Analysis
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MA202
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业核心课 Major Core Courses
6.
授课学期
Semester
春季 Spring
7.
授课语言
Teaching Language
中英双语 English & Chinese
8.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
他授课教师）
Instructor(s), Affiliation&
Contact
（For team teaching, please list
all instructors）
杨佳刚，数学系，邮箱： yangjg@impa.br
Jiagang YANG, Department of Mathematics, Email: yangjg@impa.br
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
无 NA / 待 公 布 To be announced / 已 确 定 的 实 验 员 /助 教 联 系 方 式 Please list all
Tutor/TA(s)
（请保留相应选项 Please only keep the relevant information）
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
2
授课方式
Delivery Method
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
11.
学时数
Credit Hours
48
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
数学分析 III 或数学分析精讲
Mathematical Analysis III or Real Analysis
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
复变函数论是现代数学的一个重要分支。它在数学的许多分支以及物理、工程技术领域中都有广泛的应用。本课程旨在使
学生理解并掌握复变函数的基本理论，了解复变函数的应用，体会复变函数理论之美。
The theory of functions of a complex variable is an important branch of modern mathematics. It has wide applications in many
braches of mathematics as well as in physics and engineering. This course aims to enable students to understand and grasp the basic
theory of functions of a complex variable, learn its applications, and appreciate the beauty of this theory.
16.
预达学习成果 Learning Outcomes
通过本课程的学习，学生应掌握复变函数的基本计算，掌握全纯函数、解析函数、亚纯函数等基本概念，掌握柯西定理、
柯西积分公式、留数公式等重要定理，并能够运用这些定理来解决问题。
After completing this course, students should master the basic calculation of functions of a complex variable. They should master the
basic concepts such as holomorphic, analytic, and meromorphic functions. They should also master the important theorems such as
Cauchy’s Theorem, Cauchy’s integral formula, the residue formula, and be able to solve problems using these theorems.
17.
课程内容及教学日历 （如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明
主讲人）
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
1. Preliminaries to Complex Analysis 复分析预备知识 (2 hours)
2. Holomorphic functions, Cauchy-Riemann equations 全纯函数, CR 方程 (6 hours)
2. Cauchy’s Theorem and Its Applications 柯西定理及其应用 (8 hours)
3. Meromorphic Functions and the Logarithm, residue theorem 亚纯函数与对数, 留数定理, (12 hours)
4. Entire Functions 整函数 (8 hours)
5. Conformal Mappings 共形映射 (10 hours) (最后 2 hours 用于复习)
3
18.
教材及其它参考资料 Textbook and Supplementary Readings
教材 Textbook:
Complex Analysis, by Elias M. Stein and Rami Shakarchi, 影印版，世界图书出版公司，2013 年 1 月版
其它参考资料 Supplementary Readings：
Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, by Lars V. Ahlfors
Complex Analysis, by Serge Lang
Functions of One Complex Variable, by John B. Conway
Complex Variables and Applications, by James Ward Brown and Ruel V. Churchill
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
课堂表现
Class
Performance
小测验
Quiz
课程项目 Projects
平时作业
Assignments
期中考试
Mid-Term Test
期末考试
Final Exam
期末报告
Final
Presentation
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
B. 二级记分制（通过/不通过） Pass/Fail Grading
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority
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