Midterm 1 Solutions

# 3 usipg the calculus of residues evaluate the

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ot;. 3. Usipg the calculus of residues,. evaluate the integral &quot; S 21l' cos {ne- sinlJ}. exp (coslJ) de o for all integral values of n. 4. Show that, for -1 &lt; P &lt; 1 and -Jt &lt; A &lt; Jt, the integral 00 1 X 1+ 2 x. f tAx c.er:r 5;•.. A 71 .x + xl. si&quot;, Hint: it will be helpful to write cos)., as Iff .;i- ( e i. A + f .s;1'\ ~ (Euler) e&quot; (. .A ). .. .. 5. By integrating a suitable function around a closed contour in the z-plane, evaluate the integral SihX x( X 1- + 6.. 2. ) dx ) a being a real number. 6. Evaluate the Inverse Laplace Transform of the function .... f) (\$ = s / (s 4 - a 4 ) ~; and check the limiting case a -0. ~;' / Cf)'\$ 'J-)( J~t 10 1.t ()&lt; ) 'I)} W...
View Full Document

## This document was uploaded on 02/28/2014 for the course PHYS 201 at UCSD.

Ask a homework question - tutors are online