Recent content by taylormade

Not exactly a homework problem, a problem from a sample test. I'm boning up for my qualifying exam. Homework Statement Consider the vector field: F = (ax + by)i + (cx + dy)j where a, b, c, d are constants. Let C be the circle of radius r centered at the origin and going around...

I know - because the Prof says: "Solve Using Calculus of Residues". I think I figured it out. I'm just beat from working on these - easy stuff is giving me fits.

-sigh- yes - that is what I meant. Thanks! OK - for x^6+1, there would be 6 poles, all at x^6 = -1, and they would be simple poles (right?). (well, z^6 = -1, after converting to the contour). I took those poles to be z=e^pi*i/6, e^3*pi*i/6 and e^5*pi*i/6 as the only ones contained in the...

Homework Statement Calculate \int_0^{+\infty}\frac{\x^2}{1+x^6}dx I found the poles/residues for this guy, and did the integral over the semicircular contour from -R to R, with R->infinity. I get poles that contribute at: \frac{1}{6}e^\frac{-4*pi*i}{6}...