hw1.pdf - Math 185 Homework 1 David Corwin Due Thursday September 6 in class This should go without saying but you may assume ordinary facts from

hw1.pdf - Math 185 Homework 1 David Corwin Due Thursday...

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Math 185 Homework 1 David Corwin August 28, 2018 Due Thursday, September 6 in class. This should go without saying, but you may assume ordinary facts from multivariable calculus without proof. Note: By S-S, I mean [S-S]. 1. Please complete the survey at 2. S-S Chapter 1, Exercise 1 Note: Answers can be short, but be descriptive (e.g., don’t just say “a line” or “a circle,” but describe which line or circle). 3. S-S Chapter 1, Exercise 3 4. For the next problem, we need the following definition: Definition. If f ( z ) = f ( x + iy ) = u ( x, y ) + iv ( x, y ): U C is a real differentiable function from an open subset U C to C , then we write df d z := 1 2 ∂f ∂x + i ∂f ∂y = 1 2 ∂u ∂x + i ∂v ∂x + i ∂u ∂y + i ∂v ∂y . Show that f satisfies the Cauchy-Riemann equations if and only if
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