A B2A0104

Module 111
17 a) If f(x) = > + 2 for या > ‏ر > عر‎ find the Fourier series expansion of f(x). (6)
b) Express f(x) = |x| -7 < > < 77 25 Fourier series. (5) 01२
18 a) Obtain Fourier series for the function f(x) = {८८ whenO
m(2—x) ೫1071 15252
b) Obtain the half range cosine series for f(x) = x in the 21010781 0 > ‏ع‎ > >.

1 1 1 2
Hence show that 12 + 32 + 52 + ⋅∶ =
Module 1V
19 a) Solve xp — yq = ४२ - ‏گر‎ (6) ए) Solve ०222 — 7 22 12 —_a2z2= ex-y. (5)
‏۔چھ‎ ठ्ठ dy
OR
20 ೩) 5016-9222 --ಕಜ = SinxCos2y. (6)
Ox 02017
b) Solve 9 - 2q = 33511 (y + 2x).
Module V
21 Derive one dimensional wave equation. (10)
OR

(5)

(5)

22 a) A tightly stretched homogeneous string of length | with its fixed ends at x = 0 and (10) x =1
executes transverse vibrations. Motion starts with zero initial velocity by displacing the

string into the form f(x) = k( x?- x3).Find the deflection u(x,t) at any time t.
Module VI

23 Find the temperature distribution in a rod of length 2m whose end points are (10) maintained

at temperature zero and the initial temperature is f(x) = 100(2x — x’).
OR

24 A long iron rod with insulated lateral surface has its left end maintained at a (10) temperature
0°C and its right end at x=2 maintained at 100°C. Determine the temperature as a function

of x and t if the initial temperature is u(x,0) = {100x 0100 1
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