Bondary Value Problems Using Green's Function-Mathematical Physics-Exam Paper, Exams of Mathematical Physics

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Mathematical Physics Sessional Examination-I] PAM -507 (March 14, 2011) Total marks 100 (All questions carry equal marks) Exam duration = 1.5 hours Question I. Find the particular solution of the following BVP using the Green function method d*w(x diyp(x ve). awe) dx? dx TO) = a p(0) = -3 1) = 1 Question 2. Classify the given PDE as hyperbolic, parabolic or elliptic and find the general solution SU,.x =2, Ugy -3U yy = 0 Olds FEN) EG CE 447) Question 3 Express the following vector (BP Sine set wrt) Pa (Cos6-sP 620) b 4 27 in terms of cylindrical coordinates with unit vectors (A, 8, 2) Question 4 The elliptic cylindrical coordinates are given as: U =: - / Stahu (or ¥ (4+ CoiAp hav) >} I x =acosh(u) cos(v), y =asinh(u) sin(v), z= z ys 4 fa cerhe Sav (4 Sbecesy i) 2 = 4 mi ( (a) Develop a relationship between unit vectors in elliptic cylindrical coordinates (i, #, Z) and the unit vectors (7, j, k) in Cartesian coordinates. (b) Find the scale factors for elliptic cylindrical coordinates hehe a [imvr Sob, hs | docsity.com