Differential Geometry I (미분기하학)

Class Info

Class Number: Math 372002
Dates: Sep 2 2013 - Dec 6 2013
Room: NS 318
Meeting time:
Monday 15:00 - 16:15
Friday 15:00 - 16:15

Purpose: Introduction to Differential Geometry; Curves in Space
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

The purpose of this course is to introduce basic concepts of Differential Geometry and use them to study the properties of curves in space.

Final Exam: December 13, 15:00 - 17:00, Room NS 318

The final exam is an open book written test. The range covers Sections 2.3 - 3.5 of the textbook.

Syllabus

Week Chapters Topics
1 1.1 Euclidean Space. Differentiability.
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 late October,
and a final exam in mid-December.
The grades will be accorded the following weights.
Attendance 10%
Mid-term: 40%
Final: 50%

Homework

I will assign homework each Friday for the material covered that week.
It will be due to hand in on the following Friday.
Last modified: Wed Dec 4 10:42:10 KST 2013