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.