PAPER NO. 1          
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PUT ON 20th july,2k3
                                               am-201
                              
                                  (B.Tech 3rd Semester,2063)
Time : 3 Hours                                                                                        Maximum Marks : 60
NOTE:- This paper consist of Three Sections. Section A is compulsory. Do any Four questions from
                 Section B and any two questions from Section C

                                     Section-A                                         Marks : 20

1(a) Define unit impulse function.
(b) Write Euler's formulae for a function f(x) in the interval (0,2c).
(c) Let the fourier series for the function f(x) in the interval (-c,c) be

How will it change if f(x) is an odd function.
(d) If
then prove that
(e) Evaluate using Laplace transform
(f) Form the partial differential equation from
z(x, t) = xf1(x + t) + f2(x + t).
where f1
(g) Find
(h) let f be any complex valued function of a complex variable z. Is
(i) Evaluate
where C is the semicircle arc
(j) Find the residue of 1/(z2 + a)2
at z=ia.

                                              Section-B                                          Marks:5 Each

2. If f(x)=0 for -π < x < 0
=sin x for 0 < x <π
Provew that
Hence show that
3. Evaluate Laplace transform of
4. Prove that
5. Solve
6. If

                                               Section-C                                        Marks : 10 Each


7. Evaluate.
8. A string is streached and fastened to two points / apart. Motion is started by displacing the string in the form
y = a sin
9. (a) Solve by using Laplace transform
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