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--- math121a-f23:september_13_wednesday [2023/09/13 06:04]
pzhou [primitive of a holomorphic function on $\C$]
+++ math121a-f23:september_13_wednesday [2026/02/21 14:41] (current)
@@ Line 1: / Line 1: @@
 ====== Contour Integral ======
+Reading: Boas, Ch14, section 1-5
 So, you have learned what holomorphic function looks like, and you know there are functions which are 'bad' only at a few points. What do you want to do with these functions?
@@ Line 30: / Line 32: @@
 Example: $f(z) = 1/ [(z-1)(z-2)(z-3)]$, $\gamma$ is a contour  around the two poles $1$ and $2$.
+===== Exercise =====
+. For $t \in [0, 2\pi]$, let $z(t) = e^{it}$. Compute $\int_{0}^{2\pi} 1 / (z(t)) d z(t). $
+. For $t \in [0, 2\pi]$, let $z(t) = e^{i2t}$. Compute $\int_{0}^{2\pi} 1 / (z(t)) d z(t). $
+. For $t \in [0, 2\pi]$, let $z(t) = e^{-it}$. Compute $\int_{0}^{2\pi} 1 / (z(t)) d z(t). $

Lecture Notes