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《偏微分方程基础》中英文简介
课程名称:
偏微分方程基础
课程代码:
210573
课程类别:
专业基础课
学分:
3
预修课程:
数学分析，高等代数，微分方程及实复变函数，泛函分析等
课程简介:
本课程不仅对于偏微分方程的古典理论作了严谨的介绍和论证。而且在内容概念与方法等方面注意了与现代偏微分方程知识的内在联系，对现代数学的函数论方面知识作了基本的阐述，并注意了各数学分支知识在偏微分方程中的应用。本课程涉及相关物理模型的来源与具体运用，内容丰富，方法多样，技巧性强。对于加强学生的现代数学基础知识的学习，进一步提高研究生的分析能力打下了良好的基础。
本课程的主要内容为索伯列夫空间与广义函数的概念与性质，线性椭圆型方程弱解的存在唯一性与正则性，线性抛物物型方程广义解的存在性与正则性，双曲方程的能量方法等。
Course name: Introduction to partial differential equation
Course code: 210573
Course type: Compulsory
Course credit: 3
Prerequisite: Mathematics Analysis; Real and Complex Variable Function;
Major issue: Optimization and control theory; Applicable mathematics
Course content: The course aims to provide a though grounding not only in the classical theory of Partial Differential Equations, but also the modern theory of PDEs in the concepts and methods. It covers the basics in the modern theory, and applications of real and complex functions, functional analysis and differential equations. Some of the geometrical or physics models and their background ,applications in other mathematics branches will be introduced in this course. As we will see in this course ,the concepts are full, the methods are various and the techniques are strong.
The main contents of this course involves the concepts of Sobolev Spaces and the concepts and properties of the weakly differential functions, including the existence , regularity
and uniqueness of the weak solutions of the linear elliptic equations,
Moreover the theory and applications of the groups methods to the existence , regularity of the weak solutions of the linear heat equations are given, the energy methods to hyperbolic equations are also introduced.
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