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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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