Biju Patnaik University of Technology 2009 B.Tech Electronics and Communications Engineering Mathematics III - Question Paper

To Get Latest BPUT

NEWS,Current Affairs &

Total number of printed pages -7 B. Tech

Campus Information On

BSCM 2201

Your Mob Free Of

Cost Daily.

SAY UR FRIEND

Third Semester Examination - 2008

*type JOIN IBPUT send to 567678

MATHEMATICS - III

Full Marks-70

Time: 3 Hours

*

, Answer Question No. 1 which is compulsory

and any five from the rest.

The figures in the right-hand margin

indicate marks.

WWW. ^ibP^Ut.^CsQe^me following questions precisely :

2x10

(a) Write V²u = u_xx +u_yy + u_zz in spherical

coordinates.

P.T.O.

equation

(e) Express 1 + Mn polar form.

(I) Is there any analytic function t(z) whose imaginary part is v (x, y) = * + / ad

why ? BSCWl 2201

2. A string is stretched and fastened to two end points 7t apart, If the motion is started by displacing the string in the form u (x_t 0) = a (sin(x) - sin (2x)) from which it is released at /= 0_f then find the displacement u {x, f) in BSCM 2201    3    P.T.G-

distance Jf from the left most

10

3. An insulated rod ol length I has .Is ends * and B maintained at O'C and ¹00C respectively until steady state condition prevail." the end B is suddenly reduced to 80C and the end A _is suddenly ra.sed to 20C, then find the

temperature distribution in the rod at time t.

10

4. A rectangular plate with insulated surface 10 cm Wide and so long compared to its width that it may be considered infinite in length without introducing an appreciable error. If me BSCM 2201    4

temperature distribution u (x, y) along the edge y = 0 is given by :

f20x,    0x<5

⁼ jaOilO-x), 5x<10

while the other three edges are kept at 0^eC, then find the temperature distribution at any point of the plate.    10

(b> "''^{r L}" ¹ armuiO.f: &r.' * Ihe partwi or:-V.r.'V'

van able*

6 Wnte the an*o< at-o'H-'!)^,0 ' '¹ (a) Find me ana'yi* luncf _f(z) , u(*. i) '' '*

r _

where * V'

_{(b) Flll}dtheimeaHraciionalirMr

pots 2 i0,0) io .z, = 14,0*1 sfto

7. :4. 0, tC 2. 'A 2}-    ^&

. r rt* Lisu'Gt scnes of l*e !ur,ciior.

_f    ³ ... w: tefc is valid in ttie

\z 'WZ *1

C

region 1 z -4 -r 2    -

ifoorem    ~

I ^Jt

U-