LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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M.Sc. DEGREE EXAMINATION – PHYSICS
SECOND SEMESTER – APRIL 2008
PH 2900 / 2803 – MATHEMATICAL PHYSICS
Date : 26/04/2008 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL questions. (10 x 2 = 20 marks)
- State Cauchy’s integral formula for derivative.
- Check whether is analytic or not.
- Find the Taylor expansion for a function
- State Laurent’s Theorem.
- Give two examples of periodic functions.
Is periodic or not?
- Find the Fourier transform of
- Solve , where is a constant.
- Are the set of functions are orthogonal in the limit . Expalin why?
- Show that .
- Using the knowledge of Gamma & Beta functions evaluate,
PART – B
Answer any FOUR questions. (4 x 7.5 = 30 marks)
- Derive Cauchy-Riemann equation in polar Co-ordinate System.
- a) Using Cauchy’s Integral formula,
evaluate .
- b) If is analytic in a closed region, show that .
- Expand in a series of sines with a period of 8.
- Show that the eigen functions belonging to two different eigen values are orthogonal with respect to R(x) in (a, b)
- Prove that
PART – C
Answer any FOUR questions. (4 x 12.5 = 50 marks)
- Derive Poisson’s Integral formula for circle.
- Using Cauchy’s Residue theorem,
evaluate
- a) Find the Fourier coefficients corresponding to the function
with the Period 10.
- b) Prove that
- Solve the boundary value problem,
- Using the method of Frobenius, solve Laugerre’s differential equation.
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