The Crowdmark portal for this week's homework (the assignment which is due tomorrow) is now available. Please remember that the homework is due at 3.30 PM with a hard cutoff at 4.00 PM.

In going over the problems I discovered that the first integral in question 2 was much harder than I had thought (when working through a similar problem beforehand I apparently made the rookie mistake of assuming that |sin z| <= 1 holds for complex numbers as well as real numbers!), and requires some ideas we haven't really seen yet because of the combination of the removable singularity at the origin and the trigonometric function. Given the shortness of time before the assessment comes due, I have decided to handle this by making only the setup and the evaluation of the residue worth marks; in other words, you should set up the integral the way you do those in question 1, and calculate the residue, but you don't need to show that the integral over C_R goes to zero or worry about what to do with the singularity at 0 (which actually does contribute something to the overall integral, even though it is removable). As we will see in class shortly (though maybe not today), handling the integral over C_R as well as the singularity at zero (even though it is removable) requires splitting the integral into four different pieces. This technique will become part of a problem on a future assignment.

I am thinking of moving the due date on the future assignments to Saturday; at any rate, the due date for the upcoming assignment will take into account the fact that it has not yet been posted (though I will post it soon). I will also post the lecture notes (for 5101) from last week as soon as I am able to type them.

Please let me know if you have any questions!

Nathan