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Math · Advanced Math
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Suppose that f is a function defined in R 1.e. fox xn). The Laplacian off, X1,X2,... denoted by Af, is defined to be the sum of all unmixed second derivatives f: Af 1,2, ...n w(x, y, z) is defined in R3 via w (i) Compute first and second partial derivatives of w w.rt x. o not include w in your answer.) dw/dx (i) From the computations above and the pattern seen in the expression of d2w/ax2, can you write the other two unmixed) second derivatives without doing the actual differentiation? (Do not include w in your answer.) (iii) Find the Laplacian of w. Your answer should be in terms of w only and not include any of the x,y,z variables. Aw 0.5 1.5

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