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Course Description

Course code: MATH 472 Course Name: Introduction to Differential Geometry

Credit Hours (lecture + exercises) : 4(3+1)

Level : Eiegth

Prerequisite: MATH 141

Contents:

Theory of curves in R3-Regular curves - arc length and reparametrization –Natural parametrizationSerret-Frenet apparatus – Existence and uniqueness theorem for space curves-Bertrand curvesInvolutes and evolutes-Local theory of surfaces-Simple surfaces-Coordinate transformations-Tangent vectors & tangent spaces - First and second fundamental forms– Normal and geodesic curvature – Weingarten map- Pricipal Gaussian and mean curvatures- Geodesics- Equations of Gauss and Godazzi-Mainardi.
الكتب المقررة والمراجع : (1) R. Millman &G.Parker,Elements of differential Geometry . (2) Manfredo Do Carmo: Differential Geometry of Curves and Surfaces, Birkhauser, Boston , 1992. (3) Michael Spivak: Introduction to differential Geometry, Vol. 1, 3 Edition, Addison-Wesley, 1965

الكتب المقررة والمراجع : (1) R. Millman &G.Parker,Elements of differential Geometry . (2) Manfredo Do Carmo: Differential Geometry of Curves and Surfaces, Birkhauser, Boston , 1992. (3) Michael Spivak: Introduction to differential Geometry, Vol. 1, 3 Edition, Addison-Wesley, 1965

Christian Bar, Elementary Differential Geometry, Cambridge University Press 2010