# 本科微分几何教学的一些探索Some Explorations on Undergraduate Teaching of Differential Geometry

DOI: 10.12677/AE.2019.96111, PDF, HTML, XML, 下载: 412  浏览: 694

Abstract: In this paper, we first propose some problems on the teaching of the undergraduate course of differential geometry, and then give some advice on the teaching of the course. Our advice mainly includes: enhancing the interdisciplinary knowledge and the applications of new theory, enhancing the ability of computations and graphic method, and adding contents and hours to the course.

1. 引言

2. 存在的问题

1) 缺乏微分几何与其他课程的联系

2) 缺乏抽象理论与具体实践的结合

3) 计算能力和几何直观能力不足

4) 几何课程与课时显少

3. 一些教学探索

3.1. 加强知识交叉及新理论运用

$ΙΙ=Ld{u}^{2}+2Mdudv+Nd{v}^{2}=\left(du,dv\right)\left[\begin{array}{cc}L& M\\ M& N\end{array}\right]\left(\begin{array}{c}du\\ dv\end{array}\right)$

$\iint g\left(x,y\right)\text{d}x\text{d}y=\iint g\left(x\left(u,v\right),y\left(u,v\right)\right)|\frac{\partial \left(x,y\right)}{\partial \left(u,v\right)}|\text{d}u\text{d}v$

3.2. 加强实践及计算能力

3.3. 加强几何直观

Figure 1. The orthogonal frame of surface

Figure 2. The surface S and its tangent plane X

3.4. 增加课时与课程内容

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