Vinayaka Missions University 2008 M.Sc Physics MATHEMATICAL AND NUMERICAL METHODS t (Correspondence ) - Question Paper

COURSE CODE -2030505
PG DEGREE exam – SEP 2008
M.SC (PHY)
MATHEMATICAL AND NUMERICAL METHODS
(For Candidate Admitted from Calendar 2007 Onwards)
Time: three Hours Max.Marks:75
Section-A
ans all the Questions: 15 X one = 15
1. Example for differential equation?
2. describe series?
3. Write the formula for Rodrigue?
4. describe a complex variable?
5. Example for multi valued function?
6. describe branch point?
7. The value of L F(+)
+
8. The value of L 1
S2+a2
9. describe inverse Fourier sine transform?
10. Write the formula for picards method?
11. Write the formula for Simpson (1/3) method?
12. Write the formula for Runge-kutta method?
13. Form of curve fitting?
14. describe para bell?
15. Formula for standard deviation of Poisson distribution?
Section-B
ans all the Questions: five X six =30
16. a) Derive Rodrigue’s formula?
(Or)
b) Write the generating functions?
17. a) Derive Analytic functions?
(Or)
b) Write Cauchy Reimann conditions multivalued functions?
18. a) Write the inverse laplace transform application to integral
formula ?
(Or)
b) obtain the Laplace transform of COS3 +?
19. a) Write the principle of fitting a straight line?
(Or)
b) Derive the formula for mean and standard deviation of normal
distribution?
20. a) Derive Newton- Rephson method?
(Or)
b) Derive Gauss elimination method?
Section-C
ans any 2 Questions: two X 15 = 30
21. Derive recurrence relation and orthogonally property for Bessel?
22. State and prove Cauchy’s integral theorem and formula?
23. State and prove fourier transform integral theorem and convolution
theorem?
24. Derive curve of a form Y= A XB and Y = ABX?
25. calculate Y (0.1) and Y (0.2) by R-K method of fourth order for the
differential formula
dx
dy
= xy+y2 , y (0)=1 ?

Earning:   Approval pending.