Vinayaka Missions University 2008 M.Sc Mathematics ANALYTICAL MECHANICS AND TENSER ANALYSIS :T : CORRESPONDENCE - Question Paper

COURSE CODE - 2030502
PG DEGREE exam - SEP 2008
M.SC (MATHS)
ANALYTICAL MECHANICS AND TENSER ANALYSIS
(For Candidate Admitted from calendar 2007 onwards)
Time: three Hours Max. Marks: 75
part –A
ans all the Questions: 15X1= 15
1. Write the formula for kronecker delta?
2. describe contra – variant vectors?
3. Write the formula for skew symmetric tenser?
4. Write Eules equation?
5. Write down the formula for 2nd order tenser?
6. What is transformation law?
7. provided an example for application of dynamic for space?
8. What is christoffel symbols?
9. describe Geodesic?
10. What is curvature tenser?
11. What is the difference ranging from Riemann curvature and
constant curvature?
12. Write the legal regulations of covariant differentiation?
13. Write down the formula for curl?
14. What is Gradient?
15. Write down the formula for divergence?
part – B
ans any 5 questions: five x six = 30
16. a) Express r. o . F interms of x1y1z1 provided that x=r sin F
cos F, y=sin Fsin F, Z=rcos F
(Or)
b) explain about the kroncekeer delta?
17. a)Solve ds2=9(dx1)2+8 (dx2)2+4(x3)2+16d x1 dx2+36 dx2 dx3
+ 2dx3 dx4
(Or)
b) Derive associative Tenser?
18. a)Prove that R? I, jk = R? I, jk
(Or)
b) Write the legal regulations of christoffel symbols?
19. a)State and prove Geodesic – Euleris equation,
(Or)
b) State any prove the principle of conservation of energy?
20. a)Derive the formula for Gradient, divergence, curl
(Or)
b) describe carfesian fenson and isotropic tensor, permutation
tenson and provide an example?
part – C
ans any 2 questions:- two x 15 = 30
21. obtain a geodesics on a sphere?
22. Write down the spherical co-ordinates Explain?
23. Derive (i) christoffel tensor, (ii) Ricci tenson and Einstein
tensor?
24. State and prove Gauss theorem ?
25. State and prove stokes theorem?

Earning:   Approval pending.