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0800MAT201122003

Module 2
The points of trisection of a string are pulled aside through the same distance
on opposite sides of the position of equilibrium and the string is released from
rest. Derive an expression for the displacement of the string at subsequent
time.

281 du

Solve the boundary value problem 3 = ‏كيم‎ क" 0 > ‏ع«‎ < L= (0, t)=

a
Ou
0, त (0) = 0, u(x, 0) = x
Module 3

Determine ‘a’ so that the function u = e~™

cosay is harmonic and find its
harmonic conjugate.

Rez?
Is the function f(z) = ‏ھا‎ , 2 = 0 0000100005 or not at 2 = 0
0, 2-0

Fi ⋅ ⋅ ↥↕ ⋅ 1
ind the image of the region |2 − 5 < 2 under the transformation w = ۲

Show that f(z) = |z|? is differentiable only at z = 0, hence it is nowhere
analytic.

Module 4

23-6 ⋅ ⋅ ⋅ ∙ ⋅
Evaluate $. செ where C is |z| = 1 in counterclockwise direction

Z+2
-22

Find the Maclaurin series expansion of न

sinh2z ~ + ⋅ ~ ‏جج‎
‎Integrate ಕೆ ८ dz incounterclockwise direction around the unit circle
got
2
Find the Taylor series expansion of f(z) = Tn with centre 20 = —i
Module 5
eZ

Find the Laurents series of that f(z) = that converge for 0 > |2 - 1| ಆ

(2-1)?

R and determine the region of convergence

E 27 50:30
valuate 9 ‏سے سے‎

Evaluate ழ்‌. (87122 dz counter clockwise around C :|z — 0.2| = 0.2

Find the principal value of [कतना

2k 2k 2k ‏باد عاد‎

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