MCQs of Laurent's Series & Residues (Complex Variables and Partial Differential Equations - 3130005)

Showing 1 to 10 out of 13 Questions

The Laurent series of function $f (z) = \frac{1}{z (z - 1)}$ for the region $|z| < 1$ is _____ .

The Laurent series of function $f (z) = \frac{1}{z (z - 1)}$ for the region $|z - 1| < 1$ is _____ .

The principal part of Laurent series of $f (z) = \frac{e^{z} - 1}{z^{2}}$ is _____ .

The laurent series of function $zcos (\frac{1}{z})$ about z=0 is _____ .

(a)	$z + \frac{1}{2!} \frac{1}{z} + \frac{1}{4!} \frac{1}{z^{3}} + \frac{1}{6!} \frac{1}{z^{5}} + . . . . . .$
(b)	$z - \frac{1}{2!} \frac{1}{z} + \frac{1}{4!} \frac{1}{z^{3}} - \frac{1}{6!} \frac{1}{z^{5}} + . . . . . .$
(c)	$z - \frac{1}{2} \frac{1}{z} + \frac{1}{4} \frac{1}{z^{3}} - \frac{1}{6} \frac{1}{z^{5}} + . . . . . .$
(d)	none of these

The residue of $f (z) = \frac{e^{2 z}}{z - 2}$ is _____ .

The residue of $f (z) = \frac{1}{(z - 1) (z - 3)}$ for $z = 1$ is _____ .

The residue of function $f (z) = \frac{e^{z}}{z^{3}}$ is _____ .

The residue at z=0 of function $f (z) = z \cos (\frac{1}{z})$ is _____ .

The residue at z=0 of function $e^{\frac{3}{z}}$ is _____ .

10.

What is the value of $\int_{C : |z| = 1}^{} z^{4} e^{\frac{3}{z}} d z$ ? Use the laurent's series expansion.

Showing 1 to 10 out of 13 Questions