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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI — 600 034 B.Se. DEGREE EXAMINATION —- PHYSICS FOURTH SEMESTER - NOVEMBER 2016 PH 4504/PH 4502/PH 6604 - MATHEMATICAL PHYSICS Date: 04-11-2016 Dept. No, Max. : 100 Marks Time: 01:00-04:00 PART-A Answer ALT. questions: (10 x 2 = 20 Marks) 1. Represent z = = in polar form 2. Find the value of In (—1) 3. Evaluate i 2° dz 4. What is the principle of deformation cf path? What are fundamental mode and overones of a vibratirg string? 6. Determine the value of cif u(x,t) = e7' sin 2x satisfies _ =c* = 7. Give the change of scale property of a Fourter transform. 8. Define Fourier cosine transform of a function. 9. Write the Lagrangian interpolation formula for unequal intervals 10. Compute the value of (0.02) for y' = 1 +-3* with y(0) = 0 and A = 0,02 using Euler's method. PART-B Answer any FOUR questions: (4.x 7.5 =30 Marks) 11. Find the reel and imaginary parts of tan (x + iy). sinhz 12. Evaluate f eH dz in counter clockwise where Cis the circle |z| = 2. 13. Obtain the general solution of one dimensional wave equation using product method. 14. State and prove convolution theorem for Fourier transforms 15, Evaluate g ae by dividing into 8 equal parts using Simpson’ s 13" rule. PART -¢ Answer any FOUR questions: (4 x 12.5 =50 Marks) 16. (a) Derive Cauchy-Riemann equations for a function f(z) tobe analytic. (b) Show that u = sin x cosh y is a harmonic function. (7.545) 17. (a) Evaluate le 2 dz fromz = Oto z=4+ 2i along the curve C given by z =" +it. (b) State and prove Cauchy's integral theorem (547.5) 18. Obtain the solution of two dimensional Laplace equation in electrostatic potential problem 
