LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

FG 24

SIXTH SEMESTER – APRIL 2008

PH 6604 / 6601 – MATHEMATICAL PHYSICS

 

 

 

Date : 21/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL the questions:                                                                          (10 x 2 = 20)

1. Plot  for a fixed ‘r’ and .
2. Find  a)     b) .
3. Give the condition on a function f(z)=u(x,y) + i v(x,y) to be analytic.
4. Evaluate along a straight line from i to 1+i.
5. Write down the Lplace’s equation in two dimensions in polar coordinates.
6. Write down the equation for one dimensional heat flow.
7. State Parsavel’s theorem.
8. Define Fourier cosine transform.
9. Give trapezoidal formula for integration.
10. Define the forward and backward difference operators.

PART – B

Answer any FOUR  questions.                                                                    (4 x 7\ = 30)

1. Show that the following function  is harmonic and hence find the corresponding analytic function, .
2. Prove Cauchy’s integral theorem.
3. Find D’ Alembert’s solution of the vibrating string.
4. State and prove convolution theorem in Fourier transform.   (2+5\=7\)
5. Use Simpson’s 1/3 rule to find correct to two decimal places, taking step size h=0.25.

PART – C

Answer any FOUR   questions.                                                                   (14 x 12\ = 50)

1. a) Determine  and plot its graph                                                           (3\)

1. b) Perform the following operations i) ii) and locate these values in the complex plane. (4+5=9)

1. a) State and prove Cauchy’s integral formula.

2. b) Integrate in the counter clockwise sense around a circle of radius 1 with centre at z=¹/₂. (2+5+5\=12\)

1. Derive the Laplace’s equation in two dimensions and obtain its solutions.
2. Find the Fourier transform and the Fourier cosine transform of the function

.

1. Estimate the value of f(22) and f(42) from the following data by Newton’s interpolation:

x	20	25	30	35	40	45
f(x)	354	332	291	260	231	204

 

 

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