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Complex analysis midterm 05

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Complex analysis midterm 05
(April 2, 2015)
Complex analysis midterm 05
Paul Garrett [email protected]
http://www.math.umn.edu/egarrett/
[This document is
http://www.math.umn.edu/˜garrett/m/complex/examples 2014-15/midterm 05.pdf]
Please write on one side of a page, with your name on every page.
Please restate the respective questions, and respond in complete sentences, in standard English, legibly. The
goal is explanation and also persuasion, not crypticness or telegraphic-ness.
Responses should be intelligible without definitive prior expertise.
intelligible without knowing the message(s) in advance.
That is, the message(s) should be
Questions are equally weighted.
[05.1] Exhibit a change of variables so that
Z
b
√
a
dx
=
x3 − 1
Z
B
A
√
dy
quartic in y
in terms of ℘(z) and ℘0 (z). Do not worry about explicit
determination of constants, but explication of them will get extra credit.
[05.2] For lattice Λ ⊂ C, express
1
λ∈Λ (z−λ)5
P
[05.3] Let ω1 , ω2 be a basis for a lattice Λ ⊂ C. Express ℘(z + ω21 ) as a rational function of ℘(z). Do not
worry about explicit determination of constants, but explication of them will get extra credit.
1
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