1. The final signal recovery using the process of modulation, demodulation and frequency domain filtering was found to be periodic with period and is defined by ( ) {

Find the Fourier series expansion for ( ) 2. Evaluate ∫∫ √ over the region bounded by the semi-circle lying in the first quadrant [10]

3. Find the volume bounded by the elliptic paraboloids and

4. Prove that the Fourier series expansion of the function can be expressed as ∑

. [10] 5. Evaluate the double integral by changing the order of integration in ∫∫ (

) over the positive quadrant of 6. In a two dimensional fluid flow, the stream lines is given by (

) Find the corresponding stream function and its complex potential. Also verify whether stream lines and the stream function are harmonic. Technical Mathematics 2 (M2G121464) Assignment Page 1 of 2 CALEDONIAN COLLEGE OF ENGINEERING, OMAN DEPARTMENT OF MATHEMATICS & STATISTICS

M2G121464: TECHNICAL MATHEMATICS 2 Assignment –Sem B-February 2016 7. Determine the analytic function

( ) ( ) and ( ) [10]

8. Find the Laurent's series expansion of

( b) | | √

c) | | )( )

for a) | |