Hw set 1

pg 28: 1,2, 4, 5

Hw set 2

pg 28: 6,7
pg 33: 4, 5
pg 37: 5,6

Hw set 3

pg 44: 3,4
pg 47: 1, 2, 5, 10

Hw set 4

1) We explained in class how to split the complex valued 1-form fdz into real imaginary parts U + iV. Check explicitly that ∫_γfdz = ∫_γU + i∫_γV for for every γ. 2) Check again that U, V are closed. 3) Conclude that Cauchy-Goursat theorem holds using only the above. (We have also shown in class existence of global primitive of an analytic function using the above.) From Lang: 3.2 1, 9, 10
3.5 1,2

Hw set 4

3.7 1
4.2 1,2,3