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
偏微分方程 (上)
Partial Differential Equations I
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MAT7023
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
春季 Spring
7.
授课语言
Teaching Language
英文 English
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）
王学锋，教授，数学系
慧园 3 栋 530 室
wangxf@sustc.edu.cn
0755-88018754
Wang Xuefeng, Professor, Department of Mathematics
Rm.530, Building 3, Huiyuan
wangxf@sustc.edu.cn
0755-88018754
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）
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
MA301 实变函数, MA202 复变函数，MA302 泛函分析
MA 301 Theory of Functions of a Real Variable, MA202 Complex Analysis,
MA302 Functional Analysis
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
MAT7024 偏微分方程 (下)
Partial Differential Equations II
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
学生通过本课程的学习将掌握现代椭圆与抛物偏微分方程理论中的基本概念、基本理论以及基本方法。此课将为学生们以
后阅读参考文献和开展相关的科研工作打好基础。
The students will learn fundamental concepts, theories, and methods, especially modern ones , in elliptic and parabolic partial
differential equations, and will be able to apply them to solve problems. Students will be well prepared to read more advanced
literature and carry out related research in the future.
16.
预达学习成果 Learning Outcomes
掌握现代椭圆与抛物偏微分方程理论中的基本概念、基本理论以及基本方法, 为继续学习《偏微分方程（下）》做好准
备。
The students will grasp fundamental concepts, theories, and methods, especially modern ones , in elliptic and parabolic partial
differential equations, preparing them to take the subsequent course “PDE II”.
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.)
Section 1 Classical weak and strong maximum principles for 2nd order elliptic and parabolic equations, Hopf boundary point lemma,
and their applications. （16h）
Section 2 Sobolev spaces, weak derivatives, approximation, density theorem, Sobolev inequalities, Kondrachov compact imbedding.
（16h）
Section 3 L² theory for second order elliptic equations, existence via Lax-Milgram Theorem, Fredholm alternative, L² estimates,
Harnack inequality, eigenvalue problem for symmetric and non-symmetric, second order elliptic operators. （16h）
18.
教材及其它参考资料 Textbook and Supplementary Readings
Text: Partial Differential Equations, by Lawrence C. Evans,2017
References:
1. Elliptic and Parabolic Equations, by Wu Zhuoqun,Yin Jinxue and Wang Chunpeng, World Scientific Publishing
Co.
3
2. Elliptic Partial Differential Equations of second Order, by David Gilbarg and Neil S.Trudinger, Springer.
3. Partial Differential Equations, 2nd edition, by R. McOwen, Prentice-Hall
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
40%
期中考试
Mid-Term Test
2 hours
20%
期末考试
Final Exam
3 hours
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
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