Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Engineering Mathematics 2 - Question Paper
B.E. / B. TECH. DEGREE EXAMINATIONS : APRIL / MAY 2009
CIVIL / MECH / EEE / ECE / PRODN / EIE / CSE / IT / BIOTECH BRANCHES
08C2Z2 / 08M2Z2 / 08E2Z2 / 08L2Z2 / 08P2Z2 / 08N2Z2 / 08S2Z2 / 08I2Z2
/ 08B2Z2 - ENGINEERING MATHEMATICS II
( COMMON TO PTBE )
TIME : 3 HOURS MAX. MARKS : 100
ANSWER ALL QUESTIONS PART : A
(10X2=20)
Find the complementary function of |D3 + l]y = sin 5x
2 --
Find the particular integral of [2D +1] y = 4e 2
3. Find a unit normal to the surface x2+y2-z=10 at (1, 1, 1).
4- Find VxF at(l,0,1) if F = xyz i +3x2y j +(xz2 -y2z) k.
5- Find Le_3t[2cos5t-3sinh5t]].
logfl + -' V s
Find L
7. Examine whether y+ex cosy is harmonic.
8. For what values of a and b, the function f(z) = (x-2ay) + i(x-by) is analytic.
9' Evaluate f dz
lzl~2 Z
10. Find the residue of cot Z at z = nrr where n = 0,1,2........
PART : B
(5X16=80)
(a) Solve [d2 + 4D + 8jy = e_2x + sin(2x + 3) (8) (k) Solve [x2D2-3xD + 5]y = x2sin(logx) (8)
(OR)
12 <a> o . d2y 2 t (8)
Solve ~ + y = sec x by variation of parameters, dx
(b) 2 d2y dy -> (8) Solve (1 + 2x)2 - 6(1 + 2x) + 16y = 8(1 + 2x)
dx dx
13 (a) Prove F = (y2cosx + z3)i +(2ysinx-4)j + 3xz2k is irrotational and find (8) its scalar potential.
(b) r 9 9 (8)
Verify Greens theorem for J(3x -8y )dx + (4y-6xy)dy where c is
c
the boundary of the region enclosed by the lines x=0, y=0, x+y=1
2
(8)
(8)
(4+4)
(8)
(8)
(8)
(8)
(8)
(8)
(8)
(8)
(8)
(8)
(8)
15 (a)
-1
z, = ! 2
271
d0
Evaluate J
<5 2 + cos0
20 (a)
Obtain the Laurents expansion for f(z) = region (i) |z -1| < 1 (ii) 1 < |z| < 2
(b)
00
dx
x4 +10x2 +9
Evaluate f
17 (a) If f(z)=u+iv is an analytic function and u-v=ex[ cosy - siny ], find f(z) interms of z
(b) 1
Find the image of the following under the mapping w = (i) the
z
straight line y-x+1 =0 (ii) the circle |z - 3] = 5
(OR)
18. (a) o o x
Find the analytic function f(z) = u + iv when v = x - y +
(OR)
14- (a) If F = (3x2+6y)i - 14yzj + 20xz2k , evaluate JF.dr from (0, 0, 0) to
C
(1, 1,1) along the path c where x=t, y=t2 and z=t3 (b) Verify Gauss divergence theorem for F = yi+xj + z2k over the cylindrical region bounded by x2+y2=9, z=0 and z=2.
16. (a) o < t < c
Find the Laplace transform of f(t) = { and f(t) =f(t+2c)
[2c -1, c < t < 2c
(b) Solve using Laplace transform : x -3x + 2x = 1-e2t, x(0)=1, x(0)=0.
Evaluate (i) Lte 3tsin2tJ (ii) L
Apply convolution theorem to find L
(s2 + a2j(s2 + b2)
e~3t - e *
2 2 x +y
(OR)
(b)
(b) Determine the bilinear transformation that maps z = -1, 0, 1 onto w = 0, i, 3i respectively.
19 (a) State cauchys integral formula and use it to evaluate
dz where c is the circle
valid in the
(b)
dz
1
by contour integration. (OR)
(z-1)(z-2)
|
Attachment: |
| Earning: Approval pending. |
