{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 374chw9 - HW#9 Phys374Spring 2008 Due before class Friday...

This preview shows pages 1–2. Sign up to view the full content.

HW#9 —Phys374—Spring 2008 Prof. Ted Jacobson Due before class, Friday, April 18, 2008 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374c/ [email protected] Note : Be sure to fully justify the relation between the given integral and the closed contour integral you employ in the following problems. 1. Find the residues of the following functions at the given values of z : (a) ( z + z 2 ) - 1 at 0 and at - 1. (b) z - 2 ln(1 + 2 z ) at 0 (c) [ z 3 ( z + 2) 2 ] - 1 at 0 and at - 2. (d) cos z/ (2 z - π ) 4 at π/ 2 (e) ( z 2 + 1) - 3 at ± i . Hint : See the supplement for methods of evaluating residues. [3 × 5 = 15 pts.] 2. Consider the real integral -∞ dx ( x 2 + a 2 )( x 2 + b 2 ) where a and b are positive real numbers. (a) Evaluate the integral using contour integration assuming a = b (so there are only simple poles). (b) Evaluate the integral using contour integration assuming a = b from the begin- ning (so the poles are of order 2), and then check that you recover the same result by setting a = b in the result of the previous part.

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern