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MATH 345 - DIFFERENTIAL GEOMETRY I
Fall 2002
Math345 : Differential Geometry I. A third year course.
Text book :
Elementary Differential Geometry, by Barret O' Neil. Academic Press,1997.
Other Books:
Differential Geometry of Curves and Surfaces, by
Manfredo P. do Carmo. Prentice-Hall, New Jersey , 1976.
Content:
In this period the first five
chapters of " O'Neil " will be covered. See the
"Course Syllabus" below
Course Schedule:
Tuesday 13.40-15.30 , SAZ-19
Fiday 10.40-12.30 , SAZ-19
Exams:
(%20) First Midterm Exam: November 8 (During the Lecture hours)
(%20) Second Midterm Exam: December 20 (During the Lecture hours)
(%40) Final Exam :
(%20) Homework:
see homework assigments
Subjects Covered
September 23
Tangent vectors
Directional derivatives
Curves
Differential Forms
homework assigment Set 1
September 30
Differential Forms
Mappings
October 7
Dot products and curves
Frenet Formulas
Space curves and covariant derivative
October 14
Course Syllabus
famous curves
1. Sept.23 (Sections 1.2,1.3) Euclidean Space, Tangent vectors, Directional
Derivatives.
2. Sept.30 (Sections 1.4.1.7) Curves in space, 1-forms, differential Forms,
Mappings.
3. Oct.07 (Sections 2.1- 2.3) Dot product, curves , The Serret Frenet Formulas
4. Oct.14 (Sections 2.4-2.6 Covariant derivative, frame fields, connection
forms (M.Ex.1)
5. Oct.21 (Sections 2.7,2.9) Regular Surfaces, Change of Parameters
6. Oct.28 (Sections 3.1-3.3) Isometries , the Tangent map,
orientation.
7. Nov.4 (Sections 3.5-3.7) Euclidean Geometry, Congruence of curves.
8. Nov.11 (Sections 4.1-4.4 Surfaces in R^3 , Differentiable functions
and Tangent vectors, Differential forms on surfaces. (M.Ex.2)
9. Nov.08 (Sections 4.5-4.6) Mapping of surfaces, integration of forms.
10. Nov.15 (Sections 4.7-4.8) Topological properties of surfaces, Manifolds.
11. Nov.22. (Sections 5.1-5.3) Shape operator, Normal curvature, Gaussian
curvature.
12. Nov.29 (Sections 5.4-5.5) Computational Techniques, the implicit example
(M.Ex.3)
13. Dec.06 (Sections 5.6-5.7) Special curves and surfaces, surfaces
of revolution.
14. Dec.13 Integrable Surfaces
15. Dec.20 Integrable surfaces
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Last update September 2002
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