Biju Patnaik University of Technology 2008 B.Tech (B Tech) , 3rd semester mathematics-III . - Question Paper
BPUT(B Tech) , third semester mathematics-III ques. paper. Total number of printed pages -7 B. Tech BSCM 2201
Third Semester Examination - 2008 MATHEMATICS - 111 Full Marks-70
Time: 3 Hours
Total number of printed pages -7 B. Tech BSCM 2201IWL Answer Question No. 1 which is compulsory
and any five from the rest
The figures in the right-hand margin indicate marks,
1. Answer the following questions precisely :
Total number of printed pages -7 B. Tech BSCM 22012x10
(a) Write V2u = uxx +Uyy + uzz in spherical coordinates.
Classify me partial differentia! equation
(9) Find the poles of the function
(b)
/(*) =
with respective
(2-1 ){z-zy
4 4 + Uyy- 0.
order,
(c) Test the junction :
xy
z*
f{z)=\x* + y2 o,
dz
73-
(h) Find the value or j d*.
(i) Find the value of J
lr|='
the string at a distance x from the left most end al time f. 10
3. An insulated rod oi length / has its ends A and B maintained at 0C and 100aC respectively until steady state condition prevail. If the end B is suddenly reduced to 80 C and the end A is suddenly raised to 2QC, then find the temperature distribution in the rod at time t. IWL
10
4. A rectangular plate with insulated surface is 10 cm wide and so long compared to its width that it may be considered infinite in length without introducing an appreciable error. If the BSOM 2201 4 Contd. B
temperature distribution u (x, y) along toe edge y == 0 is given by ;
[2Qx, 0<x<5
[20(10 _x), 5'x < 10
while the other three edges are kept at 0cC, then find the temperature distribution at any point of the plate. 10
Solve the following partial differential equations by Laplace transform ;
(a) ux +- 2xu( = 2x with u (xf 0) = 1 and u (0, 0 = 1 where subscript denotes the partial derivative with respect to that
variable.
and t/fO. t) - git) vtfwe $ubscnp? deooies me partial denvaifve with respect to that vanabte 5
6 Wme the answer according to the fn$iructon ,
(a) Find the analytic function
f(z) - u<x, y) 4 i,v (*- y) where u(xt yI 2xy.
IWL
(b) Find the linear fractional transform which maps iefl half iplane s 0 into ihe unit disk, 5
7. Answer as per the instruction :
(@) integrate /(z) z along the simple curve
r consists 'of straight lines joining the BSCM 2201, 6 Contd,
potnts - (0,0) to z, * f4. Ofr and z,s|4T0)to z,=(4.Z). 5
(b) Find the Lament series of the (unction
which \s valid irt the \z - 1HZ-4)
region ln< \z - 4 < 2 5
Evaluate the tallowing, integrations using residue theorem *
f *
(a) J7
0 5 + !2sin(0)
BSCM 2201 7
-C
|
Attachment: |
| Earning: Approval pending. |
