Geometry I (2014 Fall)

Course Description

The material that will be covered in the Fall semester includes (but not restricted to) the following:

這是一門兩學期的課(雖然對有些同學來說第二學期不是必修)，所以上面所列的內容不一定會在第一學期全部上完。不論上到哪裡，下學期就會從那裏開始接下去上，並且下學期還會有補充教材。

黃武雄,初等微分幾何講稿(第一卷，曲線篇，曲面篇)
A.N. Pressley, Elementary Differential Geometry. SUMS (這本書非常適合自己念，淺顯易懂)
B. O'Neill, Elementary Differential Geometry.
L.Tu, An Introduction to Manifolds, UTX.
M. do Carmo, Differential forms and applications, UTX.
S. Morita, Geometry of Differential forms.
I.M.Singer and J.A.Thorpe, Lecture notes on Elementary Topology and Geometry, UTM.
M.Spivak, A Comprehensive Introduction to Differential Geometry I.

9/16: outline, 2.2: definition of surfaces
9/18: 2.2: examples, regular value theorem
9/23: 2.2, 2.3(Tutorial: 2.2 )
9/25: 2.3: definitions (regular surfaces, differentiable functions, etc.) don't depend on the coordinate system chosen
9/30: 2.4: tangent planes(Tutorial: 2.3)
10/2: 2.4: differential of a map between surfaces
10/7: 2.5: first fundamental form(Tutorial: 2.4)
10/9: 2.5, 2.8: surface area
10/14: 2.6: orientation(Tutorial: 2.5)
10/16: 3.2: Gauss map
10/21: 3.2: differential of Gauss map(Tutorial: 2.6)
10/23: In-class presentation
10/28:3.2: second fundamental form(Tutorial: 3.2)
10/30: 3.2: Gaussian curvature, mean curvature
11/4: 3.3 (今天上兩堂) (Tutorial: 3.2)
11/6: 3.3

11/11: 今日課程合併至4號上(Tutorial: 3.3)

11/13: Midterm Chapter 2, Chapter 3.2, 3.3 (除了沒講到的部分)

11/18: 3.3, 4.3 (Tutorial: 檢討考卷)

11/20: 3.5 minimal surfaces

11/25: 3.4 vector fields(Tutorial: 3.5)

11/27: 3.4 special parametrizations

12/2: 4.2 isometry(Tutorial: 3.4)

12/4: 4.3 intrinsic geometry

12/9: 4.4 parallel transport(Tutorial: 4.3)

12/11: 4.4 geodesic

12/16: canceled for later(Tutorial: 4.2)

12/18: canceled for later

12/23: 今日課程合併至30號上(Tutorial: 4.4)

12/25: 4.4 geodesic

12/30: 4.4 geodesic curvature(今天上兩堂)(Tutorial: 4.4)

1/1: National Holiday

1/6: Review (Tutorial: review)

1/8: (3:30-6:00PM)Final Exam: Chapter 2, Chapter 3, Chapter 4.2, 4.3, 4.4 (主要是第三及第四章)

1/15: 看期末考考卷

Last Updated: December 22, 2014
URL: http://www.math.nthu.edu.tw/~nankuo/G2014.html