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Excel Engineering College

Pallakapalayam

Common to All Departments

Internal Test - II

MA2211-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

Date :19.09.2013 Time : 3 Hrs Maximum : 100 Marks

Year/sem:II/III

Answer ALL Questions

PART A(10 x 2 = 20 Marks)

1. Find the Fourier Sine Transform of

.2. Find the Fourier Cosine Transform of e

ax, x0.

3. If FC (s) is the Fourier cosine Transform of f(x), Prove that the

Fourier cosine Transform of f(ax) is

FC [

].

4. Find Fourier Sine transforms of f(x) = e3x .

5. Form the Partial Differential Equation by eliminating the

constants a and b from z= (x2+ a

2)(y

2+ b

2).

6. Solve the Partial Differential Equation pq=x.

7. Find the Particular Integral of2

2 ' '( 2 ) x yD DD D z e .8. Form the Partial Differential Equation by eliminating theconstants a and b from z= (x2+ a) (y2+ b).

9. Solve the Equation ' 3( ) 0.D D z

10. Form the PDE from (x-a)2+(y-b)

2+ z

2= r

2.

PART B(5 x 16 = 80 Marks)

11. a) i) Evaluate 2 2

0

1/ (4 )(25 )x x dx

using Transform methods.(8)

ii) Find the Fourier Cosine Transform of exp (-x2).

(8)(Or)

b) Prove That

is Self reciprocal under Fourier Sine and Cosine

Transforms. (16)

12. a) Find the Fourier Sine and Cosine Transforms of

sinx 0