Estb. 1882

University of the Punjab

MATH-306 Differential Geometry

Theory of Space Curves  Introduction, index notation and summation convention
 Space curves, arc length, tangent, normal and binormal
 Osculating, normal and rectifying planes
 Curvature and torsion
 The Frenet-Serret theorem
 Natural equation of a curve
 Involutes and evolutes, helices
 Fundamental existence theorem of space curves Theory of Surfaces
 Coordinate transformation
 Tangent plane and surface normal
 The first fundamental form and the metric tensor
 Christoffel symbols of first and second kinds
 The second fundamental form
 Principal, Gaussian, mean, geodesic and normal curvatures
 Gauss and Weingarten equations
 Gauss and Codazzi equations
Credit hours/ Marks:- 3

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