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**PYQ**Institute:
**
Biju Patnaik University of Technology BPUT
**Course:
**
B.Tech
**Specialization:
**Chemical Engineering**Offline Downloads:
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Total Number of Pages: 02
B.Tech
BSCM1205
3rd Semester Back Examination 2017-18
MATHEMATICS-III
BRANCH: AEIE, AERO, AUTO, BIOTECH, CHEM, CIVIL, CSE, ECE, EEE, EIE,
ELECTRICAL, ETC, FASHION, FAT, IEE, IT, MANUTECH, MECH, METTA, MINING, MME,
PE, PLASTIC, TEXTILE
Time: 3 Hours
Max Marks: 70
Q.CODE: B790
Answer Question No.1 which is compulsory and any five from the rest.
Th e figures in the right hand margin indicate marks.
Q1
a)
b)
c)
d)
e)
f)
g)
h)
Answer the following questions:
Define Harmonic function and conjugate harmonic ?
Define analytic function?
Find the residue of f(z) =
= 0?
(2 x 10)
Find the order of the pole of f(z) =
=0?
Let f(z) has zeros of order m and g(z) has zeros of order n , then what is the
zeros of the fg(z) ?
Find the partial differential equations by eliminating arbitrary function of
=
+ ( + )?
Write down Laplace equation in two dimension.
′
Find the complementary function of ( −
) =0;=
, ′= ?
i)
Write only the complete integral of the partial differential equations
− sin ; = , = ?
j)
Find the Radius of convergence of ∑∞ (
Q2
a)
b)
Find an analytic function whose real part is u(x, y) = 2xy + 2x ?
Evaluate ∫ ( ) ; : ⃓ ⃓ =1
Q3
a)
Solve the partial differential equations x(
) = , = ?
b)
Consider the wave equation
=
−∞ <
( , 0) = 1 then find the value of u( , ) ?
a)
′
Solve
+ ′ −2
=0?
Find the solutions of the one dimensional heat equation
with u(0, t) = u(2 , )=0 , t>0 and u(x, 0) =
?
The distribution function of
Q4
b)
Q5
a)
b)
Q6
a)
b)
(
−
)p− (
+
(5)
(5)
)q= (
< ∞ with u(x , 0) = sin
(
)
(
)
+
(5)
,
(5)
(5)
=
;
0<x<2
: ⃓ ⃓ =2?
(5)
(5)
(5)
)
) (
+
?
)!
Using Cauchy integral formula find the value of ∫
Write down the singular point of f(z) = (
=
)
What is Cauchy-Riemann equation and check whether
f(z) = ( − ) + (2 ) satisfy Cauchy Riemann equation or not?
Write down the Maclaurian series of f(z) = ?
(5)
(5)

Q7
Evaluate the real integral ∫
Q8
a)
b)
c)
Write short answer on any TWO :
Solve (D+ ′ − 1)(D+2 ′ − 2) z = 0
Solve the linear differential equation
−
Using Residue theorem find f(z)=
?
d)
Evaluate ∫
;
: ⃓ ⃓ =2 ?
(10)
?
(5 x 2)
= ( − 2 )?

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