Mathematical Physics — DU B.Sc. (Hons) Physics Previous Year Question Papers

2. Attempt five questions in all. (a) Find the Fourier series expansion for f(x) = |x| - 2<x<2 (b) Find the value of r 2). (c) Prove the relation between gamma and beta function. (d) Show that e () has no singularities. (e) Find the regular singular point of the given differential equation (f) Check whether f(z) = sinz is analytic or not. (g) If the real part of a complex analytic function is u(x,y) =x+(*2 - y'), find the corresponding imaginary part. (a) Given that f(x) =*+* for - <x<It, find the fourier expression of f(x). Deduce that (10) (b) Prove that (4) (a) Consider the following differential equation (10) Using Frobenius method, determine the roots of indicial equation and hence find the first solution. (b) Also, find the second solution. (4) (a) Prove that (6) (b) Prove that (6) (c) Evaluate the following integral using residue theorem (6) where, c is the circle |z| = 1. (b) Determine whether or not u(x, y) = 4e-3* cos3y is a solution of given differential equation: (4) (c) Prove that (4) (a) Apply calculus of residues to show that (8) (6) Find i and ay and show