1
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc.DEGREE EXAMINATION -PHYSICS
THIRD SEMESTER APRIL 2018
PH 3506- MATHEMATICAL PHYSICS
Date: 05-05-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
Part
Answer all questions (10×
1. Define an analytic function
2. Separate the following into real and imaginary part of sin x iy
3. Find the unit normal to the surface x2+y2=z at point
4. State Stoke's theorem.
5. Define Euler coefficients for even half range expansion
6. Using Laplace integral, evaluate
cosω

∞
0
7. What is a triangular matrix? Give an example
8. Determine the rank of a matrix
1 1 1
1 −1 −1
3 1 1

9. Express Gauss' integral formula and give its importance.
10. Write down the difference operator for by
Part- B
Answer any four questions. (4× marks)
11. Show − describes a circle centered at the with radius 1.
Simplify and locate it in the complex plane.
12. Using Green's theorem, evaluate
where C is boundary described counter
clock wise of the triangle with vertices
13. Obtain a Fourier expression for x for
14. Verify Cayley Hamilton theorem for the matrix
1 2 0
2 −1 0
0 0 1
and find its inverse.
2
15. Using Lagrange's interpolation formula, find the value of Y when X=10 from the following data.
X
5
6
9
11
Y
12
13
14
16
16. Use Cauchy's integral theorem to evaluate the integral where in the counter clockwise direction.
Part
Answer any four questions. marks)
17. Establish that the real and complex part of an analytic function satisfies the Laplace equation.
18. Prove that where F is a three dimensional vector in Cartesian coordinates.
Using Gauss -divergence theorem, evaluate where S is the surface of the sphere
19. write down the functional form of a square wave of period and obtain its Fourier series.
20. Determine the eigen values of A =[20−200−2−2−21] and show that matrix A satisfies its own characteristic equation.
21. Calculate the approximate value of +3−3by Simpon's1 3rd rule. Compare it with the exact value and the value obtained by Trapezoidal.
22. Find the directional derivate of g at in the direction of
If f xyz, find curl