Annamalai University 2008-3rd Year B.Sc Mathematics " 730 ANALYSIS - III " ( - VI ) ( PART - III - A - MAIN ) ( ) 5238 - Question Paper
9. (a) Prove that
4
P(m, n) =
fin fif
m + n
(b) Evaluate: 71/2cos8 0 d0.
dx
9. (a) Prove that
4
P(m, n) =
fin fif
m + n
(b) Evaluate: 71/20J
10. (a) Evaluate:
1
1 - x
0
(b) Prove that
(2n) ! n ! 4n
n +
for n = 0,1, 2, ... .
Name of the Candidate :
5 2 3 8 B.Sc. DEGREE EXAMINATION, 2008
(MATHEMATICS)
(THIRD YEAR)
(PART - III - A - MAIN)
(PAPER - VI)
(Including Lateral Entry )
December ] [ Time : 3 Hours
Maximum : 100 Marks
Answer any FIVE questions.
All questions carry equal marks.
(5 x 20 = 100)
1. Find a Fourier series expansion for the function
f(x) = x - x in -71 < x < 71.
[1+x; 0 < x < 71 [ -1 + x ; -71 < x < 0
in the range -71 to 71.
f(x)
If
71
x when 0 < x <
2
f(x) =
71
71 - x when x >
2
expand f(x) as a sine series in the interval (0, 71).
Find the Laplace transform of the following :
(a) cos2 3t.
sin at
(b)
(c) Evaluate:
|
(b) |  |
6. Using Laplace transform, solve the differential equation
d2y dy
- + 2 - 3y = sint, dt2 dt
given that y(0) = y'(0) = 0.
7. (a) Find the Fourier transform of
I a - x for I x I < a
0 for I x I > a > 0.
(b) Find the Fourier cosine transform of
f(x) = ~r Vx '
8. Solve the difference equation
Turn over
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Attachment: |
| Earning: Approval pending. |
