Unformatted text preview: ⊆ C be an open set. Let f be continuous on Ω. Show that if Z ∂R f = 0 for every ∂R ⊂ Ω, boundary of a rectangle R ⊂ C (note that Ω may not be simply connected and R may not be contained in Ω), then f has an antiderivative on Ω, ie. there exists an analytic F on Ω such that F = f . (b) Does the following function have an antiderivative on A (0;4 , ∞ )? z ( z-1)( z-2)( z-3) (c) Does the following function have an antiderivative on A (0;4 , ∞ )? z 2 ( z-1)( z-2)( z-3) Date : December 6, 2007 (Version 1.0); posted: December 6, 2007; due: December 10, 2007. 1...
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This note was uploaded on 08/01/2008 for the course MATH 185 taught by Professor Lim during the Fall '07 term at Berkeley.
- Fall '07