(Established
under section 3 of UGC Act, 1956)
Course
& Branch: B.E /B.Tech- Common to ALL Branches
Title
of the paper: Engineering Mathematics –
IV
Semester:
IV Max. Marks: 80
Sub.Code:
6C0054/401 Time: 3 Hours
Date: 22-04-2008 Session: FN
PART – A
(10 x 2 = 20)
Answer All the Questions
1. Find Fourier series given f(x) = x in - p £ x £ p.
2. Define complex form of Fourier Series.
3. Form Partial differential equation by eliminating ‘f’ from
z =
f(x3 – y3)
4. Find the complete solution of 
5. State any
two assumptions in the derivation of one dimensional wave equation.
6. Define a2 in ut
= a2 uxx.
7. State the
two dimensional heat equation in Cartesian as well as polar co-ordinates.
8. Write the
three positive solutions of the Laplace
equation in polar co-ordinates.
9. State
Convolution Theorem of Fourier Transform.
10. If F{f(x)}
= 
then Prove that 
then Prove that
PART – B (5 x 12 = 60)
Answer All the Questions
11. Find the fourier Series expansion of f(x) of
period ‘l’.
Hence deduce the sum of the series 
(or)
12. Find first three harmonics in the Fourier
Series of y = f(x)
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
|
y
|
1.0
|
1.4
|
1.9
|
1.7
|
1.5
|
1.2
|
1.0
|
13. Solve (y + z) p + (z + x) q = x + y.
(or)
14. Solve (D2 – 2DD/ + D/2)z
= x2 y2 ex+y where 
15. Solve ytt
= a2yxx 0 £ x £ l, t > 0 subject to y (0, t) = 0 y(l, t) = 0, yt(x, 0) = 0
(or)
16. A rod of
length 20cm has its ends A and B kept at 30°C and 90°C respectively until steady state conditions prevail.
If the temperature at each end is then suddenly reduced to 0°C and maintained so, find the temperature u(x, t) at a
distance ‘x’ from A, at any time ‘t’.
17. An
uniformly ling metal plate in the form of an area is enclosed between the lines
y = 0 and y = p for positive values of x. The temperature is zero along the edges y =
0 and y = p and the edge at
infinity. If the edge x = 0 s kept at temperature ‘ky’, find the steady state
temperature distribution in the plate.
(or)
18. A semi
circular plate of radius a has its boundary dimeter kept at temperature zero
and circumference at f(q) = k, 0 < q < p. Find the steady state temperature at any distribution point of the
plate.
19. Find Fourier Transform of the distribution
Hence evaluate 
(or)
20. Find
Fourier Sine and Cosine Transform of e-ax a > 0, and hence find
Fourier Sine Transform of 
and Fourier cosine
transform of 
and Fourier cosine
transform of 
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