Wednesday, August 27, 2008

Mathematics assignment Q.No-3

PMR INSTITUTE OF TECHNOLOGY
MATHEMATICS –III (MA1201)
IIyr AERONAUTICAL
ASSIGNMENT NO: 3


Questions
1. Find Z[1/(n+1)(n+2)]
2. Find the inverse Z transform of [4Z/ (Z-1)³] using long division.
Hint: (a-b) ³=?
Ans: F (Z) =∑2n (n-1) Zˉⁿ
f (n) =2n(n-1)
3. Using partial fraction Zˉ¹ [Z/Z⁴-1]
4. Using Zˉ¹ [(4Z³-3Z²+3Z)/ (Z-1)³] by residue method.
5. Using convolution theorem… find Zˉ¹ [Z²/(Z-1)³] Ans: n(n+1)/2
6. Solve U n+2-5Un+1+6Un=(-1)ⁿ with u0=u1=0
Ans: Un= (1/12) (-1) ⁿ-(1/3)2ⁿ+ (1/4)3ⁿ