Daily Assignment for Wednesday, April 2

Due Friday, April 4 on Canvas.

• Remember that \( \cot(\pi z) \) has poles at all integers. Where are the poles of \( \cot(\pi^{-1} z^{-1}) \) ? What is the residue of \( \cot(\pi^{-1} z^{-1})dz \) at the origin? This may be a trick question.
• In class, I sketched two arguments for why holomorphic functions are infinitely differentiable, but I said that both of these arguments were incomplete. Explain for yourself what the logical gaps were. How specific can you be about what the remaining work is?
• Do exercises 2 and 10 on p. 506 of Needham.
• Assign yourself a grade for this assignment :
  1. At least 60 minutes.
  2. About 45 minutes.
  3. About 30 minutes.
  4. About 15 minutes.
  Submit your grade as a submission comment with your assignment. This comment must be the first comment and it must be exactly 1 character long or the grade won't be registered.