## December 17, 2011

### MATHEMATICS 3 JNTU previous years question papers

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

1. (a) Prove that (2n+1)x Pn(x) = (n+1)Pn+1(x) + nPn−1(x).
(b) Show that x4 = 1
35 [8P4(x) + 20P2(x) + 7P0(x)]. [8+8]

2. (a) Find where the function
i. w = 1
z
ii. w = z
z −1
ceases (fails ) to be analytic.
(b) In a two dimensional fluid flow, the stream function ψ = tan−1 (y/x), then find velocity potential function φ [8+8]

3. (a) Separate into real and imaginary parts log cos ( x + iy )
(b) Determine all values of ( 1+ i )i [8+8]

4. (a) Evaluate RCRezdz, where C is the shortest path from 1+i to 3+2i.
(b) Use Cauchy’s integral formula to evaluate H
c
z−1
(z+1)2(z−2)dz where ‘c’ is the circle
|z − i|= 2 [8+8]

5. (a) Find the Taylor’s series expansion of sin z = π/2.
(b) Find the Taylor’s series expansion of ez about z = 3. [8+8]

6. (a) State and prove Cauchy’s Residue theorem.
(b) Find the residue at z = 0 of the function
f(z) = 1+ez sin z+z cos z [8+8]

7. Evaluate R
C
f1(z)
f(z) dz by using the Augument principle where C is a circle
|z| = 4 and f(z) = (z2+1)2
(z2+2z+2)3 [16]

8. (a) If w = 1+iz
1−iz find the image of |z| < 1.
(b) Find the image of the unit circle |z| = 1 under the linear fractional transformation w(z) = 2iz−2−2i
(1−i)z−1 [8+8]

## FEEL USEFUL PLEASE GIVE +1

#### Post a Comment

Get Syllabus in your Mail

## Total Pageviews

Privacy Policy
http://topengineeringcollegesintamilnadu.blogspot.com use third-party advertising companies to serve ads when you visit our website. These companies may use information (not including your name, address, email address, or telephone number) about your visits to this and other websites in order to provide advertisements about goods and services of interest to you. If you would like more information about this practice and to know your choices about not having this information used by these companies, click here.