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Estelar: Faculty of Engineering

1. The document is an exam for a Faculty of Engineering course covering mathematics topics including partial differential equations, Fourier series, and Z-transforms. 2. It contains two parts - Part A with 10 short answer questions worth a total of 25 marks, and Part B with 6 longer problems worth a total of 50 marks. 3. The questions cover a range of advanced calculus and differential equations concepts tested in the exam.

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97 views1 page

Estelar: Faculty of Engineering

1. The document is an exam for a Faculty of Engineering course covering mathematics topics including partial differential equations, Fourier series, and Z-transforms. 2. It contains two parts - Part A with 10 short answer questions worth a total of 25 marks, and Part B with 6 longer problems worth a total of 50 marks. 3. The questions cover a range of advanced calculus and differential equations concepts tested in the exam.

Uploaded by

apex predator
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Code No.

6009

FACULTY OF ENGINEERING
B.E. 2/4 (CE/EE/Int/ECE/M/P/AE/CSE) I – Semester (Main.) Examination, December 2013
Subject: Mathematics – III
Time: 3 Hours Max.Marks : 75

Note: Answer all questions from Part – A. Answer any five questions from Part – B.
PART – A (25 Marks)
1. Form a partial differential equation by eliminating the arbitrary function f from
z = eax+by f(ax-by). 3
2. Reduce the partial differential equation z2(p2+q2) = x2+y2 to the form
f(x,p) = g(y,q). 2
3. Find ao in the Fourier series expansion of f(x) = e-x in (-1,1). 2

4. If x = b
n 1
n sin nx, 0 < x <  , then find bn. 3

5. Solve py3+qx2 = 0 by the method of separation of variables. 2

6. Solve
u
x
4
u
y ar
, u(0,y) = 8e-3y.

7. Find the iterative formula to find N using Newton-Raphson method.


8. If f(1) = -3, f(3) = 9, f(4) = 30 and f(6) = 132, then find f(x).
9. Find the Z transform of {n an}.
3

2
3
3
el
10. Find the convolution {2n ∗ 3n}. 2

PART – B (50 Marks)


11.(a) Solve y2p – xyq = x (z-2y). 5
t
(b) Solve q(q2+s) = pt by Monge’s method. 5
Es

  ,    x  0
12. Find the Fourier series expansion for f(x) =  and hence
 x , 0  x  
1 1 1
find the sum 2  2  2  ... 10
1 3 5
2 2
 u  u
13. Solve  =0, 0 < x, y <  subject to u(0,y) = u(  ,y) = u(x,  ) = 0
x 2 y 2
and u(x,0) = sin2 x. 10

14.(a) Solve the system of equations 4x – 3y – 9z + 6w = 0, 2x + 3y + 3z+6w= 6


and 4x – 21y – 39z – 6w = -24 by Gauss elimination method. 5
dy
(b) Find the approximate value of y(1.3) for = -2xy2, y(1) = 1 using Euler’s
dx
method. 5
2
7z  11z
15.(a) Find the inverse Z transform of . 5
(z  1)(z  2)(z  3)
(b) State and prove convolution theorem of Z transforms. 5

16. Solve pxy + pq + qy = yz by Charpit’s method. 10


17.(a) Find the Fourier series expansion of f(x) = | cos x| in [-  ,  ]. 5
dy
(b) Find at x = 0.5 from the following table. 5
dx
x: 0 1 2 3
y: 1 3 15 40

****

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