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Pune University - Sem - I : Methods of Mathematical Physics, April 2010

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Total No. of Questions : 7] P882 [Total No. of Pages : 3 [3722]-103 M. Sc. PHYSICS PHY UTN - 503 : Methods of Mathematical Physics (New Course) (2008 Pattern) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory. Attempt any four questions from the remaining. 2) Draw neat diagrams wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic table and pocket calculator is allowed. Q1) Attempt any four of the following : [16] a) What are spherical harmonics? State the orthogonality condition satisfied by them. b) Let W be the subspace of R4 generated by {(1, 2, 5, 3), (2, 3, 1, 4), (3, 8, 3, 5)}. Find the basis and dimensions of W. c) Prove Schwartz inequality for vectors in an inner product space. d) State and prove Parseval s identity for Fourier series F(x). e) Find the Laplace transform of the function 2 = cos t f (t ) = 3 = 0 f) 2 t> , 3 2 ,t< 3 Show that the function f(z) = z2 is an analytic function of z. P.T.O.

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Additional Info : M.Sc. PHYSICS, PHY UTN - 503 : Methods of Mathematical Physics (New Course) (2008 Pattern), Pune University
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