Class InfoClass Number: Math 372002Dates: Sep 3 2012  Dec 8 2012 Room: NS 318 Meeting time:
Purpose: Introduction to Differential Geometry; Curves in Space Text: Barrett O'Neill, Elementary Differential Geometry, Rev. 2nd Ed., Elsevier 2006 

Week  Chapters  Topics 
1  1.1  Euclidean Space. Differentiability. 
2  1.23  Tangent Vectors. Directional Derivatives. 
3  1.4  Curves in R^3. 
4  1.56  1Forms. Differential Forms. 
5  1.7  Mappings. 
6  2.1  Dot Product. 
7  2.23  Midterm Exam. Curves. The Frenet Formulas. 
8  2.4  ArbitrarySpeed Curves. 
9  2.56  Covariant Derivatives. Frame Fields. 
10  2.78  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. 
Attendance  10% 
Midterm:  40% 
Final:  50% 