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MAT7068 偏微分方程 (上)
MAT7068 PDE I
课程学分/学时
Course Credit/Hours
苏琳琳助理教授
Assistant Prof. Linlin Su
是否面向本科生开放
Open to undergraduates
or not
本科课程:MA303 偏微分方程,MA301 实变函数,MA302 泛函分析
Undergraduate courses: PDE, Real Analysis (Lebesgue Theory), Functional
Analysis
(如面向 本 科 生开放, 请 注 明 区 分 内容 。 If the course is open to undergraduates, please indicate the
difference.)
以介绍偏微分方程的基本理论和方法为主并结合该领域的科研前沿介绍一些具有应用背景的例子.
The main part of this course consists the basic theories and methods of partial differential equations. Some
examples with application background from the research frontier in this field will also be introduced.
(如面向本科生开放,请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.)
以板书教学为主.
Mainly blackboard-chalk teaching.
教学内容
Course Contents
(如面向本科生开放,请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.)
Classical weak and strong maximum principles for 2nd order elliptic
equations, Hopf boundary point lemma, and their applications
Classical weak and strong maximum principles for 2nd order parabolic
equations, Hopf boundary point lemma, and their applications
Sobolev spaces, weak derivatives, approximation, density theorem
Sobolev inequalities, Kondrachov compact imbedding
L² theory for second order elliptic equations, existence via Lax-Milgram
Theorem, Fredholm alternative
An example in homogenization theory