btechktu.blogspot.in btechktu.blogspot.in btechktu.blogspot.in
A B1A003 Total No. of pages:2

Reg. No. Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
THIRD SEMESTER B.TECH DEGREE EXAMINATION, DEC 2016

Course Code: MA201
Course Name: LINEAR ALGEBRA AND COMPLEX ANALYSIS

Max. Marks: 100 Duration:3. Hours
PARTA
(Answer any two questions)
1.൨ Show that u = y? — 3x?yis harmonic and hence find its harmonic conjugate. (8)
b Find the image of |2 − ;| < Sunder the transformation = = . Also find the fixed points

Nie

of the transformation w = (7)
2.2 2൦൧൦ an analytic function and prove that an analytic function of constant modulus is
constant. (8)

b Find the linear fractional transformation that maps മ = 0, 22 = 1, 23 = ०0010

w, = —1, w2 = —i,w3 = 1 respectively. (7)
3.a Show that f(z) = 0710059) - ie *siny 15 differentiable everywhere. Find
its derivative. (8)

b Find the image of the lines x = c and y = k, where c&kare constants, under the
transformation w = sinz. (7)
PART 8

(Answer any 1110 questions)

4.8... Evaluate J. Re (z) dz where C is a straight line from 0 to 1 + 2i. (7)
co dx 7
b Show that ۲ ಇತ್‌ ಶ್‌ (8)
2
3.8... Integrate = counterclockwise around the circle |z - 1 - ‏|ز‎ = न by Cauchy’s
Integral Formula. (7)
‏حا‎ Evaluate [8 dz where C is |z — 2 — i| = 3.5 by Cauchy’s Residue Theorem

(8)

6൧ Iff(z= = find the Taylor series that converges in |z — ट| ಆ Rand the Laurent’s

series that converges in |z — i| > R. (8)
b Define three types of isolated singularities with an example for each. (7)
Page 1௦12

btechktu.blogspot.in btechktu.blogspot.in btechktu.blogspot.in