Ma6251 MATHEMATICS III

ANNA UNIVERSITY QUESTION PAPER NOVEMBER / DECEMBER 2018

1. i Reg. Nas i

Question Paper Code : 20749

B.B/:Tech, DEGREE ENAMINATION, NOVEMBER/DECEMBER 2018,
Second Semester
Civil Engincecing
MA 6251 — MATHEMATICS — IT

(Common to Mechanical Engineering (Sandwich), Aeronautical Engineering,
Agriculture Engineering, Automobile Engineering, Biomedical Engineering,
Computer Seienco and Engineering, Electrical and Electronics Engineering,

Electronics and Communication Engineering, Electronics and Instrumentation

Engineering, Environmental Engineering, Geoinformatics Engineering, Industrial

Engineering, Industrial Engineering and management, Instrumentation and
Control Engineering, Manufacturing Engineering, Materials Science and.
Enginedring, Mechanical Engineering, Mechanical and Automation Engineering,
‘Mechatronics Engineering, Medical Electronics Engineering, Petrochemical
Engineering, Production Engineering, Robotics and Automation Engineering,
Biotechnology, Chemical Engineering, Chemical and Electrochemical Enginoering,
Fashion Technology, Food Technology, Handloom and Textile technology,
Information Technology, Petrochemical Technology, Petroleum Engineering,
Pharmaceutical Technology, Plastic Technology, Polymer Technology, Textile
‘Chemistry, Textile Technology, Textile Technology (Fashion Technology)

(Regulations 2013)
‘Time: Throo hours ‘Maximum : 100 marks

Answer ALL questions.

PART A = (10% 2= 20 marks)

1. Find grad at the point (1, ~

Dior

16 F=axisbyj+cek and $ is the surface of a sphere of unit radius, find
ffFias

3, Find the particular integral of (D~2)*y = 6%.

4, Solve the equation z’y'- a + y 20.

ionic /ASOGATEPROFESOR/NEGUNEALENCIEERING / RM COLLEGE OP ENGINEERING AND TECHNOL

2. 5, Find the Laplace transform of fü) if /(0,

feat Sts
tor
1

Or

6 Find Dt

7. Determine whether the Cauchy-Riemann conditions are satisfied for the
function w= 22?

8. Find the fixed points of the transformation

10, State Cauchy's Residue theorem.
PART B— (6 x 16 = 80 marks)

LL. (0) @ Show that F=(iny+2)i+(xeosy-2)j+(e-y)k is conservative
force field, Hence find its scalar potential. ®

(O. Using Shen. theorem, evaluate fFar, where

Fé ey')i-2oj and C is the rectangle bounded by x=20.
y=, y=b. o

or
©) Apply Gauno divergence theorem to evaluate [EAS for
risas db Gey cian ®

6) Using Greon's theorem, evaluate fay > Ye 4 rh], where C ia
thee edo ginny y and yet ©

2 20749

IC /ASOCATE PROFESSOR [MEGA ENCIERRO COLLEGOP ENGINEERING AND TECHNOLOGY. 2

3. 12 @
©
13. @
œ
M 6)
o

0)

o

co)

0

0

(0)

0

ao

css e, 2+ x = 081 given that x
Save: De y oi, Sax x cot given that 0) 22, 9020.)
Solve: (D +2D- My inde 4e" ©
or
pr eri 10y~ 6%
Solve: ar £2 200049) 125 6 ®
à D
ve by method of variation of parameter 74 y sect.
Suave by method of variation ofparameter Là» o
Solve (Dis2D+Dy=te* given 0)=1 and y0)=-2 using
Laplace ténor. ®
Find the Laplace transform of ©
or
Find the Laplao transform ofthe period function of period aif
1 O<tcal2 ss
ro, O and fsa) = 10) o

Using convolution theorem find the inverse Laplace transform of
1

ETES u

Find the bilinear transformation that maps the points 2 = =, i,0

into the points w ®

If f(2)=u-iv is an anlaytic function of 2=x+iy, prove that
Ve 2

a Byres Are ®
Or

Find the " analytic function whose imaginary part is

e'(esiny+ 70). ©

Find the mas fhe ring under tara 1

fo Wn
lexe2, pere 10]

3 20749

inc ASOCATE PROFESOR [GG ENEIERING / RK COLL OP EXCUSA TECHNOLOGY

4. 15. @ @
«iy

© @
(0)

de-2

Find the Laurent series expansion of — 2 in the region

4 (2+1)2(2-2) =

idees. o

ing Cauchy’ residue theorom, evaluate [pá wi

es eee Ye [eyecare ser

© isthe ide fe-4 + Q]
or

rate [Ez de where O da the are reife? ine

Cauchy integral formula. o

Bvaluate tates using Contour integration o

4 20749

in ASOCATE PROFESSOR GUAM ENCINEERING / RK COLLEGE OF ENGINEERING AND TECHNOLOGY,