K L University 2009 B.Tech Computer Science and Engineering Model Mathematics IV - Question Paper
KONERU LAKSHMAIAH COLLEGE OF ENGINEERING
Autonomous
Model ques. Paper
Mathematics – IV
II B.Tech (I Sem)
KONERU LAKSHMAIAH COLLEGE OF ENGINEERING
Autonomous
Model Question Paper
Mathematics IV Time : 3hrs
II B.Tech (I Sem) (Common to CSE & ECE) Max. Marks : 60
Note: Answer all questions. All questions carry equal marks.
UNIT - I
1. (a) Define Fourier series of a function in (a,a + 2p)
Find the Fourier series of x x2 in (-p, p) (1+5) M
(b) Expand f(x) = e-x as a Fourier series in the interval (-c, c).
OR
2. (a) Obtain cosine and sine series for f(x) = x in the interval 0 x p.
Hence show that 6M
(b) Derive Parsevals formulae.
UNIT
- II
6M
3 (a) Find the Fourier transform of
f(x) = 1 for |x| < 1
0 for |x| > 1 (4+2) M
(b) Find the Fourier transform of , for - < x < . 6M
OR
4 (a) Find the Fourier sine and cosine series of (3+3) M
f(x) = 1 for 0 x < a
0 for x a
(b) Prove that psinq if 0 q p 6M
0 if q p
UNIT - III
5 (a) From the following table of values of x and y , obtain for x = 1.2. 6M
x |
1.0 |
1.2 |
1.4 |
1.6 |
1.8 |
2.0 |
2.2 |
y |
2.7183 |
3.3201 |
4.0552 |
4.9530 |
6.0496 |
7.3891 |
9.0250 |
(b) From the following table of values of x and y , obtain for x = 3 6M
x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
y |
6.9897 |
7.4036 |
7.7815 |
8.1291 |
8.4510 |
8.7500 |
9.0309 |
OR
6 (a) Evaluate by simpsons 1/3 rule with 4 strips and 8 strips respectively. 6M
(b) Compute the values of I by using trapezoidal rule with h = 0.25. 6M
UNIT - IV
7 (a) Using Taylors series method solve = x + y, given y=0 when x=1, to x=1.2 with h=0.1. 6M
(b) Solve =1 + xy, given that y=1 when x=0 in (0, 0.5) for h = 0.1 by using Picards method. 6M
OR
8 (a) Apply Runge Kutta method of Forth order to solve the following equation.
, y(0)=1. obtain y when x = 0.2 6M
(b) Solve the boundary value problem y11 64y + 10 = 0 with y(0) = y(1) = 0
by the finite difference method
UNIT - V
6M
9 (a) Define set and prove that if A,B and C are sets
(i) Ax(B C) = (A x B) (A x C)
(ii) A(BC) = (AB) (A C) 6M
(b) If A and B be two sets. If f: AB is one, onto then f-1 : B A is also one one and onto 6M
OR
10. (a) Define Equivalence relation.
Is the relation is brother of an equivalence relation on a set of human beings ? why? (1 + 5) M
(b) Define group of a non empty set G. Show that the set N of all natural numbers is not a
Group with respect to addition. (1 + 5)M
Earning: Approval pending. |