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

Attempt Four questions in all. Some useful formulae are given at the end. 𝑉 where 𝑉 is the volume of the sphere of radius 4 using spherical polar coordinates. (b) Find the period of (i) tan 𝑛𝑥 and (ii) cos 2𝜋𝑥 0 using beta and gamma functions. (e) Locate and name the singularity for 𝑥3𝑦′′ + 2𝑥2𝑦′ + 𝑦 = 0. (f) Write Parseval’s identity for Fourier series. (a) Find the unit vectors 𝑒𝑟 ̂ for spherical coordinate system in terms of 𝑖̂, 𝑗̂, 𝑘 . Also solve for 𝑖̂, 𝑗̂, 𝑘 in terms of 𝑒𝑟 (b) Represent the vector 𝐴 = 2𝑦𝑖̂ − 𝑧𝑗̂ + 3𝑥𝑘 in terms of spherical coordinates and determine 𝐴𝑟, 𝐴𝜃 and 𝐴∅. (5) 3. (a) Represent 𝑓(𝑥) = 𝑥2 in the interval −𝜋 < 𝑥 < 𝜋 in form of Fourier series. (10) 0 𝑐𝑜𝑠5𝜃 𝑑𝜃 using beta and gamma functions. (5) − 𝑦 = 0 around 𝑥 = 0 by Frobenius method. (15) 5. (a) Derive the recurrence relation 𝑛𝑃 𝑛(𝑥) = 𝑥𝑃 𝑛 (b) Expand 𝑥2 in series of Legendre polynomials. (7.5) Some useful formulae: Legendre Polynomials: