02000MA201092002

Pages: 2

Reg No.: Name:

Max. Marks: 100

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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Third semester B.Tech examinations (S) September 2020

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

PARTA
Answer any two full questions, each carries 15 marks
2
Check whether the function f(x +iy)= ತೀ x,y = 0, / (0) = 0 1
continuous at the origin.
Find an analytic function f(z) =u+iv whose real part is € >(‰ ८05)» +

ysiny)
Check whether (2) = 108 2 is analytic.

Show that w = = maps the real axis of z-plane into the circle |w| = 1 and the
half plane y > 0 into the interior of the unit circle |w| = 1 in the w-plane
Find the image of the infinite strip -2 2 under the mapping w = €:
Find the image of the line ‏بر‎ — x + 1 = 0 under the mapping w = :
24115
Answer any two full questions, each carries 15 marks

22+22-2
2-4

Evaluate ந்த dz where 0: |z| = 5, using Cauchy’s Integral formula.

Evaluate 3) + y)dx + () — x)dy] along a straight line from (1,1) to (1,2)

and then to (4,2)

Find the Laurent series expansion about the singularity z = 1 for the function
22

(2-1)2(243)

Fi ர 1
ind the pole and residue of ಷಾ

Using Cauchy’s residue theorem evaluate f dz where 0 is |z - 2| =

22
C (z-1)2(z+2)
2

5 46
valuate |" ‏عب‎

02 +5 {7126

PART ட்‌
Answer any two full questions, each carries 20 marks

Using Guass elimination method, solve the equations x + 2y + 32 —w = 10,
2x + ‏برق‎ —3z-w=1,2x - ‏بز‎ + 22 + 3w =7,3x + 29 — 42 + 3w = 2.

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Duration: 3 Hours

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