Complex Variables and Partial Differential Equations (3130005)

Cauchy Residue theorem

BE | Semester3 Topic : Cauchy Residue theorem

Q3 (b) Summer-2020
Evaluate using Cauchy’s residue theorem $\int_{C} \frac{e^{2 z}}{{(z + 1)}^{3}} d z$ , Where, $C : 4 x^{2} + 9 y^{2} = 16$ .

4 Marks

Unit : Laurent’s series

Q3 (c) Summer-2020
Expand $f (z) = \frac{1}{z (z - 1) (z - 2)}$ valid for the region $(i) |z| < 1, (ii) 1 < |z| < 2$ and $(i) |z| > 2 .$

7 Marks

Unit : Laurent’s series