1. (2%) The asymptotic formula cos (x – 7) is a good approximation to Jo (x) for which values of x? (a) Small x, that is

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1 2 The Asymptotic Formula Cos X 7 Is A Good Approximation To Jo X For Which Values Of X A Small X That Is 1 (214.66 KiB) Viewed 25 times

1. (2%) The asymptotic formula cos (x – 7) is a good approximation to Jo (x) for which values of x? (a) Small x, that is, 0 < x <1 (b) Large x, that is, x > 1 (c) All positive x 2. (2%) The functions Jo (jo,nx) and Jo (10mx), m = n, are orthogonal in which inner product? (a) (f,8) = So'f (x)g (x) dx (b) (4,8) = So®F (x)g(x) dx (C) (5,8) = So' xf (x)g (x) dx (d) (8,8) = 6*xf (x)g (x) dx (e) None of the above. = = = 3. (2%) Which of the following partial differential equations is not separable? (a) ux + uy = 0 (b) uxx + xuyy = 0 (c) uxx + (x + y) uyy = 0 (d) ux = Uyy (e) All of the above are separable. 4. (2%) When solving the heat equation, which (if any) terms in an expansion in eigenfunctions Un are negligible at large values of t? (a) All terms remain important at large t. (b) Terms with the largest eigenvalues kĩ become negligible when t becomes large. (c) Terms with the smallest eigenvalues kbecome negligible when t becomes large. (d) There is no discernable pattern to which terms can be neglected. 5. (2%) If one looks for a space-time product solution 4 (r, t) = S(r) T (t) to the Schrödinger equation др + V (r) 4 = i at after separation of variables one finds a pair of differential equations for S and T. Which of the following is the correct equation set? (Let A be a real separation constant, which might be positive or negative.) (a) įV2S + (1 – V(r)) S = 0 and a = -AT (b) { V25 + (1 - V(r)) S = 0 and = AT (c) { vềs + (1 - V (r)) S = 0 and = -iNT (d) { V2S + (1 - V(r)) S = 0 and 47 = iAT (e) None of the above. 2024+ = =