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Unformatted text preview: shaped. Whichever be the reason, we often find it desirable to transform an equation written in one coordinate system to one valid in another cordinate system. For these tasks the method illustrated above can be helpful. 2.15. GEOMETRIC INTERPRETATION OF COVARIANT DERIVATIVES Consider now a vector field v defined at every point of space in a region R. Let the vector at the point P(0,02,03) be (1) v(P) = .i(P)g;(P). At a neighboring point P(0 + do1, tJ2 + do2, 03 + do3), the vector becomes v(P) = v(P) + dv(P) = [.P) + dvi(P)][gz(P) + dgi(P)]. On passing to the limit d0; + 0, we obtain the principal part of the difference and the derivative...
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- Fall '05