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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc.DEGREE EXAMINATION -PHYSICS
THIRD SEMESTER APRIL 2018
16UPH3MC01- MATHEMATICAL PHYSICS
Date: 03-05-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
PART- A
Answer ALL questions: (10 X 2 =20 marks)
1. Express in the form of a+ib.
2. Verify that f x2-y2+2ixy is analytic.
3. Define scalar point function.
4. Find m so that the vectors and are co-planar.
5. What do you mean by orthogonality of trigonometric system?
6. What is the fundamental period of
7. Distinguish between ordinary and partial differential equation
8. Write down a homogenous first order partial differential equation in two variables.
9. Using Trapezoidal rule, evaluate from the following data
X
0
0.5
1
1.5
2
Y
1.000
0.800
0.500
0.308
0.200
10. Given dydx with y 1 at x 0 find y (0.02) using Euler's method.
PART- B
Answer any FOUR questions: X 7.5 =30 marks)
11. Derive Cauchy Riemann equation.
12. A vector field is given by x2y) show that the field is irrotational and find the scalar potential.
13. Determine the Fourier series of the function on if x with a period of 2
14. Obtain the solution of the wave equation using the method of separation of variables
15. Obtain the Lagrange's interpolation polynomial of degree two for the following data:

16. Use Green's theorem to evaluate where, c is the boundary described counterclockwise of the triangle with vertices
2
PART C
Answer any FOUR questions: X 12.5 =50 marks)
17. State and prove Cauchy's integral theorem.
Verify the integral theorem where c is a circle of radius 1.
18. Evaluate over the area bounded between the circles r=2cos and r 4 cos
19. Find the Fourier sine integral for e-βx hence show that e-βx ∫λsinλxβ2+λ2∞0 dλ.
20. Write a one dimensional heat equation and derive its general solution.
21. Derive Newton's forward interpolation formula.Use it to find the value of y at 0.23 from the following table.
x
0.20
0.22
0.24
0.26
0.28
0.30
y
1.6596
1.6698
1.6804
1.6912
1.7024
1.7139
22. Given that for find the Fourier series of