Introduction to Differential Geometry (3+1) credit-hours: Theory of curves in R3. Regular curves and reparametrization, Serret-Fernet apparatus and theorem, existence and uniqueness theorems for space curves. Local theory of surfaces: Simple surfaces, coordinate transformations, tangent vectors and tangent spaces, first and second fundamental forms, normal and geodesic curvatures, Weingarten map, principal, Gaussian and mean curvatures. Geodesics, equations of Gauss and Codazzi-Mainardi. Prerequisite: 202M and 242M
