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
数学物理方法 Mathematical Methods in Physics
2.
授课院系
Originating Department
物理系 Department of Physics
3.
课程编号
Course Code
PHY203-15
4.
课程学分 Credit Value
4
5.
课程类别
Course Type
专业基础课 Major Foundational Course
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）
石兴强，助理教授，物理系
第二科研楼 226 室
SHI Xingqiang, Assistant Professor, Department of Physics
Rm. 226, No. 2 Research Bldg.
shixq@sustech.edu.cn
0755-88018206
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
待公布 To be announced
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
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
11.
学时数
Credit Hours
58
6
无
无
64
2
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
高等数学 A 下（MA102B），大学物理 B 下（PHY105B），线性代数 A（MA107A）
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
本课程为物理专业基础课，是部分专业核心课的先修课程。
This course is a Major Foundation Course of physical 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.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
数学物理方法是物理专业的必修基础课。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物理问题。
As the Major Foundation of physical courses, this course aims to introduce how to use mathematics as a tool & technique
to deal with physical problems. From the course, students should transform from learning pure mathematics to using
mathematics as a tool to treat real physical 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 calculation, and formulate physical problems into mathematical language in differential equations and boundary
conditions.
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). 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
3
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
1). 复函数和双曲函数
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
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
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；解的特征
第 9 周：期中考试
4). 偏微分方程：分离变量法
第 10 周：分离变量法、解的叠加
4
第 11 周：极坐标系下的分离变量法
5). 常微分方程的级数解
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
第 14 周：Legendre 函数, 连带 Legendre 函数
第 15 周：球谐函数
第 16 周： Bessel 函数
18.
教材及其它参考资料 Textbook and Supplementary Readings
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
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
30%
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
5
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
物理系教学指导委员会
Education Instruction Committee of Physics department
