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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
M.Sc.DEGREE EXAMINATION PHYSICS
FIRSTSEMESTER APRIL 2018
17/16PPH1MC04/PH 1820 MATHEMATICAL PHYSICS I
Date: 30-04-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
PART A
Answer ALL the Questions (10x2=20)
1. Write the algorithm of Runge-Kutta method of solving differential equations.
2. Write down the expression associated with Euler's method.
3. Express in the form of
4. State the condition for which the function is analytic.
5. Show that a real antisymmetric tensor has independent elements.
6. Define norm of a vector and show that
7. Show that
8. Write the terms contained in the expression for three dimensional space.
9. Define gamma function.
10. Sketch the graph for spherical Bessel's function.
PART-B
Answer any FOUR Questions (4x7.5=30)
11. Solve using Regula Falsi method.
12. Evaluate where using Cauchy's residue theorem.
13. Show that scalar product of two vector spaces satisfies Cauchy-Schwarz inequality.
14. Prove that is an invariant, if contravariant vectors and is a covariant tensor
ii) Prove that transformation of tensors form a group.
iii) Show that, if a tensor is symmetric with respect to two indices in any coordinate system, it will remain symmetric with respect to these two indices in any other coordinate system.
15. Evaluate using gamma and beta function.
ii) Show that
16. Derive any two recurrence relations of Bessel's function.
PART-C
Answer any Four questions (4x12.5=50)
17. Apply Gauss-Seidal method to solve

Correct up to decimal places, taking
18. Using contour integration show that
2
19. Diagonalize the matrix𝐴=|−22−321−6−1−2
20. If are two tensors, show that
ii) Show that in a Cartesian coordinate system, the contravariant and covariant components of a vector are identical.
iii) Derive the components of Moment of inertia tensor.
21. Solve Legendre's differential equation by Frobenius power series method.
22. Solve by Gauss elimination method