K L University 2009 B.Tech Computer Science and Engineering Model Mathematics IV - Question Paper

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