Total Number of Pages: 02
3rd Semester Back Examination 2017-18
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
Answer Question No.1 which is compulsory and any five from the rest.
Th e figures in the right hand margin indicate marks.
Answer the following questions:
Define Harmonic function and conjugate harmonic ?
Define analytic function?
Find the residue of f(z) =
(2 x 10)
Find the order of the pole of f(z) =
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 ( −
, ′= ?
Write only the complete integral of the partial differential equations
− sin ; = , = ?
Find the Radius of convergence of ∑∞ (
Find an analytic function whose real part is u(x, y) = 2xy + 2x ?
Evaluate ∫ ( ) ; : ⃓ ⃓ =1
Solve the partial differential equations x(
) = , = ?
Consider the wave equation
( , 0) = 1 then find the value of u( , ) ?
+ ′ −2
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
< ∞ with u(x , 0) = sin
: ⃓ ⃓ =2?
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) = ?