Homework  assignments  for  M361
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Nr Section : Problems
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[1]    1.2 : 2,4,6,8,10,18,24         Jan 14 → Jan 21
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[2]    1.3 : 2,4,8,20,26,28           Jan 21 → Jan 28
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[3]    1.4 : 7,8,11,14,15,18,21       Jan 28 → Feb 11
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[4]    1.5 : 18a-c,19,23,27a-b        Feb 11 → Feb 18
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[5]    1.6 : 2,3,10
       2.1 : 2a,3,7                   Feb 18 → Feb 25
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[6]    2.1 : 4,12,13
       2.2 : 1,5,9   (see R1 below)   Feb 25 → Mar  6
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[7]    2.3 : 1,2,7,10                 Mar  4 → Mar 18
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[8]    2.4 : 1,5,13,14,17             Mar 18 → Mar 25
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[9]    2.5 : 2,3,5,10
       3.1 : 3,4,6                    Mar 25 → Apr  1
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[10]   3.1 : 14
       3.2 : 1,3,5b,8                 Apr  1 → Apr  8
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[11]   3.2 : 13,18
       3.3 : 1a,1d,4,9,11             Apr  8 → Apr 15
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[12]   4.1 : 2a,8
       4.2 : 3,5,10                   Apr 15 → Apr 22
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[13]   4.3 : 3,8,20                   extra problems


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REMARKS R1 .. 

Denote by C the set of all complex numbers.

Definition.
A bounded subset of C is said to be simply connected
if both the set and its complement are connected.

Theorem. (Cauchy's theorem)
Let A be a simply connected bounded open subset of C,
and let f: A→C be analytic.
If γ is a closed piecewise C1 curve in A,
then the integral of f along γ is zero: ∫γf(z)dz=0

R1. For the problems in Section 2.2 you can use Cauchy's theorem above.
You may take for granted that disks and rectangles are simply connected.