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
工程数学
Engineering Mathematics
2.
授课院系
Originating Department
电子与电气工程系
Department of Electronic and Electrical Engineering
3.
课程编号
Course Code
EE207
4.
课程学分 Credit Value
4
5.
课程类别
Course Type
专业基础课 Major Foundational Courses
6.
授课学期
Semester
秋季 Fall
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）
何志海, 讲席教授，电子系
工学院南楼 430
hezh@sustech.edu.cn
HE Zhihai, Chair Professor, Department of Electronic and Electrical Engineering
Room 430 Engineering Building South
0755-88018510
游昌盛，助理教授，电子系
工学院南楼 708
youcs@sustech.edu.cn
You Changsheng, Assistant Professor, Department of Electronic and Electrical
Engineering
Room 708 Engineering Building South
0755-88015873
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
待公布 To be announced
2
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
11.
授课方式
Delivery Method
讲授
Lectures
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
学时数
Credit Hours
64
0
0
0
64
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
高等数学（下）A；大学物理B（下）；线性代数A
Calculus II A
General Physics B (II)
Linear Algebra A
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
本课程为电子专业基础课，是部分专业核心课的先修课程。
This course is a Major Foundation Course of EEE courses, to prepare for the
mathematics expected in more advanced physical courses.
14.
其它要求修读本课程的学系
Cross-listing Dept.
无 NA
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
本课程教授学生如何使用数学工具和技术来解决物理问题；使学生学到相关基础知识，并引导学生从纯数学的学习转到将
数学应用于实际工程问题。
As the Major Foundation of EEE courses, this course aims to introduce how to use mathematics as a tool & technique to
deal with engineering problems. From the course, students should transform from learning pure mathematics to using
mathematics solve actual engineering problems.
16.
预达学习成果 Learning Outcomes
掌握复变函数、数学物理方程和特殊函数的基本概念和理论。能用留数定理计算积分、提高抽象思维能力和符号运算能
力、以及能把物理问题写成数学方程和边界条件等。
Master functions of a complex variable, ordinary and partial differentials closely related to physical problems and special
functions. Master using the residue theorem to calculate definite integrals; improve abilities in abstract thinking and
symbolic analysis.
3
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). 复函数和双曲函数（8学时）
第1周：复数运算、极坐标表示、de Moivre’s 定理
第2周：复函数（对数、幂级数），复数简单的应用、微分和积分，双曲函数
2). 复变量函数的微积分（16学时）
第3周：复变函数、复变函数微分、Cauchy–Riemann 关系
第4周：复数项幂级数，多值函数，函数的奇点、零点
第5周：复变函数的环路积分，Cauchy 定理、 Cauchy 积分公式
第6周：Taylor级数和Laurent级数、留数定理、用留数定理计算定积分
3). 偏微分方程：通解和特解（12学时）
第7周：重要的偏微分方程、通解、通解和特解
第8周：波动方程、扩散方程；
第9周：解的特征； 期中考试
4). 偏微分方程：分离变量法（8学时）
第10周：分离变量法、解的叠加
第11周：极坐标系下的分离变量法
5). 常微分方程的级数解（8学时）
第12周：二阶线性常微分方程
第13周：常点的级数解、奇点的级数解
6) 特殊函数（12学时）
第14周：Legendre 函数, 连带 Legendre 函数
第15周：球谐函数
第16周： Bessel 函数
1). Complex numbers and hyperbolic functions
Week 1: Manipulation of complex numbers, Polar representation of complex numbers, de Moivre’s theorem
Week 2: Complex logarithms and complex powers, Applications to differentiation and integration, Hyperbolic functions
2). Complex variables
Week 3: Functions of a complex variable, The Cauchy–Riemann relations
Week4: Power series in a complex variable, Multivalued functions and branch cuts, Singularities and zeros of complex
functions,
Week 5: Complex integrals, Cauchy’s theorem, Cauchy’s integral formula
Week 6: Taylor and Laurent series, Residue theorem, Definite integrals using contour integration
3). Partial differential equations: general and particular solutions
Week 7: Important partial differential equations, General form of solution, General and particular solutions
Week 8: The wave equation, The diffusion equation, Characteristics and the existence of solutions
Week 9: Midterm examination
4). Partial differential equations: separation of variables
Week 10: Separation of variables: the general method, Superposition of separated solutions
Week 11: Separation of variables in polar coordinates
5). Series solutions of ordinary differential equations
Week 12: Second-order linear ordinary differential equations
Week 13: Series solutions about an ordinary point, Series solutions about a regular singular point
6) Special functions
Week 14: Legendre functions, Associated Legendre functions
Week 15: Spherical harmonics
Week 16: Bessel functions
18.
教材及其它参考资料 Textbook and Supplementary Readings
4
教材：
Mathematical Methods in the Physical Sciences, by Mary L. Boas. The third Edition; Wiley
其他参考资料：
Mathematical Methods for Physics and Engineering; Third Edition; K.F. RILEY, M.P. HOBSON and S. J.
BENCE; Cambridge university press
Essential Mathematical Methods for Physicists; Hans J. Weber and George B. Arfken; Academic Press
Teaching materials:
Mathematical Methods in the Physical Sciences, by Mary L. Boas. The third Edition; Wiley
Other references:
Mathematical Methods for Physics and Engineering; Third Edition; K.F. RILEY, M.P. HOBSON and S. J.
BENCE; Cambridge university press
Essential Mathematical Methods for Physicists; Hans J. Weber and George B. Arfken; Academic Press
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
15
课程项目 Projects
平时作业
Assignments
15
期中考试
Mid-Term Test
30
期末考试
Final Exam
40
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
十三级等级制 Letter 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
电子与电气工程系
5
Department of Electronic and Electrical Engineering
