微分几何

发布单位:伯明翰大学联合学院 发布时间:2023-12-14

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.