Loyola College B.Sc. Physics April 2009 Mathematical Physics Question Paper PDF Download

       LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

XC 15

B.Sc. DEGREE EXAMINATION – PHYSICS

FOURTH SEMESTER – April 2009

PH 4502 – MATHEMATICAL PHYSICS

 

 

 

Date & Time: 24/04/2009 / 9:00 – 12:00  Dept. No.                                                  Max. : 100 Marks

 

 

 

PART-A                                                             (10 x 2 = 20 MARKS)

 

ANSWER ALL QUESTIONS.

 

1). Given z1 = 2 – i and z2 = 2 + i find z1* z2 .

2). Check if the function f(z) = x + i y  is analytic.

3). Evaluate .

4). Explain the property of linearity in complex line integral.

5). Define the eigen value problem for the operator .

6). Write down the two dimensional wave equation.

7). Give the Parseval’s identity for Fourier transforms.

8). Define Fourier sine transform.

9). Why is Lagrange’s interpolation advantageous over Newton’s interpolation?

10). Write down Simpson’s 1/3 rule for integration.

 

PART-B                                                             ( 4 x 7.5 = 30 MARKS).

 

ANSWER ANY FOUR QUESTIONS.

 

11). Simplify the following a). (4+ 2i) (2 + i) ; b). 4[(2+2i)/(2-2i)]2 – 3[(2-2i)/(2+2i)]2,

Locate these points in the complex plane.

12). Verify Cauchy’s integral theorem for the integral of  z 2 over the boundary of the

rectangle with vertices (0,0) , (1,0) , (1,1), (0,1) in the counterclockwise sense.

13). Find D’Alembert’s solution of the wave equation for a vibrating string.

14). Prove the following for the Fourier transforms F{f(ax)}= (1/a)F(s/a) and F{f’(x)}= is

F(s), here F(s) is the Fourier transform of f(x) and the prime denotes differentiation

with respect to `x’.

15). Use Euler method to solve with y(0) = 2 Find y(0.2) with h = 0.1.

 

PART-C                                                             (4 x 12.5 = 50 MARKS)

 

ANSWER ANY FOUR QUESTIONS.

 

16). State and prove Cauchy’s integral formula.

17). Derive the Cauchy Riemann equation for a complex function to be analytic. Express

it in polar coordinates.

18). Explain the method of separation of variables to solve the one dimensional wave

equation .

Check whether u = x2 – y2 satisfies the two dimensional Laplace equation.

19). (a). State and prove the convolution theorem for the Fourier transforms.

(b). Find the Fourier sine transform of e-ax.

  1. (a). Given y = sin (x ) , generate the table for x = 0 /4 and /2 Find the value of

sin (/6). using Lagrange’s interpolation method.

(b). For the given data calculate the Newton’s forward difference table.

(x,y): (0,0), (1,2), (2,6), (3,16).

 

Go To Main Page

 

Latest Govt Job & Exam Updates:

View Full List ...

© Copyright Entrance India - Engineering and Medical Entrance Exams in India | Website Maintained by Firewall Firm - IT Monteur