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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc.DEGREE EXAMINATION -PHYSICS
FOURTH &SIXTH SEMESTER APRIL 2018
PH 4504 PH 4502 PH 6604- MATHEMATICAL PHYSICS
Date: 09-05-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
PART A
Answer ALL questions (10 x 2 20 Marks)
1. Express the function in the form
2. Determine the principal value of the argument of the complex number
3. State some of the basic properties of line integral.
4. Evaluate c is the circle
5. Write down one Dimensional heat equation and a suitable separable solution for the same.
6. What is the basic difference between the solution of one dimensional wave equation and
one dimensional heat equation?
7. State Parseval's theorem.
8. Define Fourier Transform and Inverse Fourier Transform.
9. Write down the Lagrange's formula to find if three sets of values and are given.
10. State Simpson's rule.
PART B
Answer any FOUR questions x 7.5 30 Marks)
11. Verify by direct substitution that Re and Im satisfy Laplace's Equation.
12. State and prove Cauchy's integral formula.
13. Applying the method of separation of variables techniques, find the solution to the P.D.E.
2
14.Obtain Fourier Cosine Transform of 0
15. By dividing the range into ten equal parts, evaluate by Trapezoidal rule and Simpson's one third rule. Verify your answer with direct integration.
PART C
Answer any FOUR questions x 12.5 50 Marks)
16. Prove that
(b)Find the general value of
17. Evaluate along the two paths: straight line joining and
18. Derive the solution of wave equation by Alembert's method.
19. State and prove the convolution theorem on Fourier Transforms.
(b)Find the Fourier transform of
20.(a) Using Newton's forward interpolation formula, find f(1.5) from the following data
(b)Given with y 1 for x 0. Find y approximately for x 0.1 by Euler's method in
five steps.