MA530_JAN96

MA530_JAN96 - (horizontal strip of width 2 π symmetric...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MA 530 QUALIFYING EXAMINATION January 1996 Name: 1. Find all singular points of the following functions and classify them: a) cot z - 1 z b) sin ± exp 1 z ² c) 1 z 2 - 1 cos πz z +1 2. Find the Laurent expansion of 1 ( z - 1) 2 ( z +2) in the annulus 1 < | z | < 2. 3. Evaluate the residue Res ln z - 1 z +1 for each branch of this function which is defined in a neighborhood of . 4. Find a conformal map of the following region onto the upper half–plane:
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (horizontal strip of width 2 π , symmetric with respect to R , from which the positive ray is removed). 5. For all real t evaluate the integral Z 1+ i ∞ 1-i ∞ e tz z 2 + 1 dz (the path of integration is the vertical line { z : Re z = 1 } ). 6. Show that the series ∞ X n =0 cos nz n ! is uniformly convergent on every compact in C ....
View Full Document

This document was uploaded on 01/25/2012.

Ask a homework question - tutors are online