A couple notes about the homework:

-- For those of you in 5101: we will discuss the idea behind Q2 in class tomorrow; it is actually quite simple and is described in Goursat, Section 45.

-- Q3: the two lecture sections are a bit out of sync; the idea is that all of you should be able to do at least one of these two integrals. Please only submit one solution! If you submit more than one, you will get the mark on whichever one gets marked first (which may be entirely random).

-- Q3, first integral: initially I (mistakenly) thought that this integral could be evaluated using the same contour as was used for evaluating the Fresnel integrals. It turns out that one needs to look instead for a second line segment the integral along which can be written in terms of the original integral, and then solve. (This is fairly close to the technique used for the second integral in this question.) Also owing to this there does not seem to be any simple way to evaluate the original integral as given, but only the integral with sin (x^2) replaced by cos (x^2) - sin(x^2). I have updated the homework assignment to reflect this change. (Please note that I do mean sine of the square of x, not the square of the sine of x!)

Please let me know if you have any questions!

Nathan