Geometry I (2019 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.

9/10(二): outline, 2.2: definition of surfaces, examples
9/11(三): (Tutorial: 第一週不上習題課)
9/12(四): 移課到 12/3, 12/10
9/17(二): 2.2, 2.3: regular value theorem
9/18(三): (Tutorial: 2.2)
9/19(四): 2.3: definitions (regular surfaces, differentiable functions, etc.) don't depend on the coordinate system chosen
9/24(二): 2.4: tangent planes, differential of a map between surfaces
9/25(三): (Tutorial: 2.3)
9/26(四): 移課到 9/10, 9/17
10/1(二): 移課到 9/24
10/2(三): (Tutorial: 2.4)
10/3(四): (Update:生病取消，下週三習題補課)
10/8(二): 2.5: first fundamental form, surface area
10/9(三): (Tutorial: 補課 2.6: orientation)
10/10(四): National Holiday
10/15(二): 3.2: Gauss map
10/16(三): (Tutorial: 2.5, 2.6)
10/17(四): 3.2: differential of Gauss map, second fundamental form
10/22(二): 3.2: Gaussian curvature, mean curvature, Dupin indicatrix
10/23(三): (Tutorial: 2.6, 3.2)
10/24(四): 3.3: Gauss map in local coordinate
10/29(二): 移課到 10/8
10/30(三): (Tutorial: 3.2)
10/31(四): 移課到 10/15,10/22

11/5(二): Midterm:Chapter 2, Chapter 3.2

11/6(三): (Tutorial: 檢討考卷)

11/7(四): 3.3: calculating the principal direction and the asymptotic direction

11/12(二): 3.3: Geometric meaning of the Gauss curvature

11/13(三): (Tutorial: 3.3)

11/14(四): 3rd fundamental form, calculus of variation

11/19(二): 3.5: minimal surface

11/20(三): (Tutorial: 3.3, 3.5)

11/21(四): 3.5, 3.4: vector fields

11/26(二): 移課到 11/5

11/27(三): (Tutorial: 3.5)

11/28(四): 移課到 11/12, 11/19

12/3(二): 3.4: special parametrizations

12/4(三): (Tutorial: 3.4)

12/5(四): 4.2: isometry, 4.3: intrinsic geometry

12/10(二): 4.4: parallel transport

12/11(三): (Tutorial: 4.2)

12/12(四): 4.4: parallel transport, 4.4: geodesic

12/17(二): 4.4: geodesic

12/18(三): (Tutorial: 4.3)

12/19(四): 4.4: geodesic

12/24(二): 移課到 12/17

12/25(三): (Tutorial: 4.4)

12/26(四): 4.4: geodesic curvature

12/31(二): Review (多上一堂)

1/1(三): (Tutorial: National Holiday)

1/2(四): (3:30-5:30PM)Final Exam: Chapter 2, Chapter 3, Chapter 4.2, 4.3, 4.4 (主要是第三及第四章)

1/10(五): 看期末考考卷 11:00am-12:00

Last Updated: January 1, 2020
URL: http://www.math.nthu.edu.tw/~nankuo/G2019.html