微分几何
学分:3学分
先修课程:实分析与微积分;向量、几何与线性代数;多元微积分与向量分析
课程描述:
本科课主要介绍微分流形的基本概念,流形间映射的性质,并且会讨论一系列例子。接下来引入向量以及向量场,给出常微分方程系统解的存在性定理以及相关的单参数群作用。另外会详细介绍共变张量以及微分形式,并得到流形上的可积性定理。
成绩评定方式:
评定:学期总评成绩(100%)
重评:补考卷面成绩(100%)
成绩评定要求出勤率
参考教材:
陈维桓 编著,微分几何,北京大学出版社,2006.01,讲义随堂提供。
Differential Geometry
Credits: 3 Credits
Pre-requisite: Real Analysis & the Calculus; Vectors, Geometry & Linear Algebra; Multivariable & Vector Analysis
Description:
The basic concept of differentiable manifold is introduced along with mappings of manifolds and their properties; a fairly extensive discussion of examples is included. Then we introduce vectors and vector fields and with a careful exposition for the existence theorem for solution of systems of ordinary equations and the related one-parameter group action. Covariant tensors and differential forms are treated in some detail and then used to develop a theory of integration on manifolds.
Methods of Summative Assessment:
Assessment: Assessments done during semester (100%)
Reassessment: best of 3 hour resit examination (100%)
Attendance at tutorials is a required element of this module
Recommended textbooks:
Chen Weihuan, Differential Geometry, Peking University Press, 2006.01.
Detailed lecture notes will be provided to students.