Differential Geometry (미분기하학)

Class Info

Class Number: Math 372
Dates: Aug 31 2009 - Dec 04 2009
Room: NS 318
Meeting time:
Monday 10:30 - 11:45
Friday 9:00 - 10:15

Text: Barrett O'Neill, Elementary Differential Geometry, Rev. 2nd Ed., Elsevier 2006
Links
Homework
Material covered
Leonard Susskind on General Relativity: Lecture 1 of 15

Final Exam: Friday December 11, 9:00 - 11:00, Room NS318

Syllabus

Week Chapters Topics
1 1.1 Euclidian Space.
2 1.2-3 Tangent Vectors. Directional Derivatives.
3 1.4 Curves in R^3.
4 1.5-6 1-Forms. Differential Forms.
5 1.7 Mappings.
6 2.1 Dot Product.
7 2.2-3 Midterm Exam. Curves. The Frenet Formulas.
8 2.4 Arbitrary-Speed Curves.
9 2.5-6 Covariant Derivatives. Frame Fields.
10 2.7-8 Connection Forms. The Structural Equations.
11 3.1 Isometries of R^3.
12 3.2 The Tangent Map of an Isometry.
13 3.3 Orientation
14 3.4 Euclidean Geometry
15 3.5 Congruence of Curves. Final Exam.

Grading

We will have a mid-term test in October, a conference report in November,
and a final exam in December.
The grades will be accorded the following weights.
Attendance 10%
Conference: 15%
Mid-term: 30%
Final: 45%

Homework

I will assign homework on Friday for the material covered that week.
It will be due to hand in on the following Friday.
Last modified: Mon Nov 30 12:42:48 KST 2009