00084___e6ff09436c6b6527adc1276b586ab0fc - Sec 2.16 2.22 P...

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Sec. 2.16 PHYSICAL COMPONENTS OF A VECTOR 63 2.22. Prove that the Laplacian of Prob. 2.18 can be written Hint: Use the results of Prob. 2.21. 2.23. Show that the covariant differentiation of sums and products follows the usual rules for partial differentiation. Thus, (+vr)li +,ivr + +v'li, (vrV,)li = (vPvr), i = vr(ivr + vrv,li, (AijBmn)Ir = Aij(,Bmn + AijBmn(r, where a comma indicates partial differentiation. Remember that the covariant derivatives of a scalar are the same as the partial derivatives. Derive the transformation law for the Euclidean Christoffel symbols I':B(d,x2,x3). Ans. Under a transformation of coordinates from xi to Z', the Euclidean metric tensor transforms as 2.24. Differentiating both sides of the equation with respect to
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