Homework  assignments  for  M361
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Nr Section : Problems
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[1]    1.2 : 2,4,6,8,10,18,20,24      Aug 25 → Sep 1
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[2]    1.3 : 2,4,8,20,26,28
       1.4 : 11,14                    Sep 1 → Sep 8
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[3]    1.4 : 8,15,18,19,20,21
       1.5 : 1,9                      Sep 9 → Sep 15
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[4]    1.5 : 18a-c,19,23,27a-b        Sep 15 → Sep 29
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[5]    1.6 : 1,3,10
       2.1 : 3,7                      Sep 29 → Oct 6
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[6]    2.1 : 4,12,13
       2.2 : 1,5,9   (see R1 below)   Oct 6 → Oct 20
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[7]    2.3 : 1,2,7,10
       2.4 : 1,2,5,17,19              Oct 20 → Nov 3
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[8]    2.5 : 2,3,5
       3.1 : 3,4,6,14                 Nov 3 → Nov 10
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[9]    3.2 : 1,3,5b,8,13,25
       3.3 : 1a,1d,4,14,18            Nov 10 → Nov 24
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[10]   3.3 : 19
       4.2 : 10,15
       4.3 : 3,8,20                   Nov 24 → Dec 1
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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.