فاطمه محمد مصطفى العظمى

Math 374: Differential Geometry ( 4 hour course)

Prerequiste: Math 202 and Math 242.

Book for the course: Elements of Differential Geometry, by R. Millman and G. Parker.

Chapter 1 is a review and you must read it, we will cover basically chapters 2 and 4 in detail. This is a long computational course and you should practice solving lots of problems, in order to understand the course.

Description of the course:

1-Theory of curves in R^3, regular curves and reparametrization.

2- Serret-Fernet frame and theorems.

3- Existence and uniqueness theorems for space curves.

4- Local theory of surfaces. simple surfaces, coordinate transformations.

5-Tangent vectors and tangent spaces.

6- first and second fundamental forms, normal and geodesic curvatures.

7- Weingarten map, principal, Gaussian and mean curvatures. Geodesics equations of Gauss.

Home Works:

To get the list of home work questions, please click here.

Solutions To Some Homework Problems: Click here

Old Exams: To get a list of some old exams, click here.

Some usefull links:

http://ocw.mit.edu/OcwWeb/Mathematics/18-950Spring-2005/CourseHome/index.htm

http://www.dmoz.org/Science/Math/Geometry/Differential_Geometry/

http://en.wikipedia.org/wiki/Talk:Contact_geometry

http://xahlee.org/SpecialPlaneCurves_dir/Intro_dir/familyIndex.html

Exams:

First mid term  is out of 20 points

Second mid trem is out of 20 points

Home work: 10 points.

Final exam is out of 50 points..