Daily Assignment for Wednesday, March 19

Due Friday, March 21 on Canvas.

• Do exercises 12 and 13 on p. 479 of Needham.
• Do exercises 8.11 and 8.13 on pp. 151–152 of Howie.
• In class, we proved that if \( f \) is a \( \mathbb R \)-differentiable function on a simply connected domain \( U \) and if \( \gamma \) is the boundary of a region \( V \) inside \( U \) then \( \int_\gamma f dz = 2i \int_V \frac{\partial f}{\partial \bar z} dA \). Write \( f \) as \( u + iv \) and express \( \frac{\partial f}{\partial \bar z} \) in terms of \( \frac{\partial f}{\partial x} \) and \( \frac{\partial f}{\partial y} \) to obtain a proof of Green's theorem.
• Optional reading : §9.3.5.
• 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.