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Title: Residue
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 32 | Residue
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Bright video: https://youtu.be/zCdNE4JGPKg
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Dark video: https://youtu.be/CVRIO9LKtxw
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Original video for YT-Members (bright): https://youtu.be/BuEoOYbiH04
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Original video for YT-Members (dark): https://youtu.be/yLRx9F_vmLw
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: ca32_sub_eng.srt missing
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $f: D \rightarrow \mathbb{C}$ be a holomorphic function that has an isolated singularity at $z_0$. What is the correct definition of $\mathrm{Res}(f, z_0)$?
A1: $ \frac{1}{2 \pi i} \oint_{\partial B_{\varepsilon}(z_0)} f(z) , dz $
A2: $ \frac{1}{2 \pi} \oint_{\partial B_{\varepsilon}(z_0)} f(z) , dz $
A3: $ 2 \pi i \oint_{\partial B_{\varepsilon}(z_0)} f(z) , dz $
A4: $ \oint_{\partial B_{\varepsilon}(z_0)} f(z) , dz $
Q2: Let $f: \mathbb{C}\setminus { z_0 } \rightarrow \mathbb{C}$ be given $f(z) = \frac{1}{z - z_0}$. What is the value of the residue $\mathrm{Res}(f, z_0)$?
A1: $1$
A2: $ \frac{1}{2 \pi} $
A3: $ 2 \pi i $
A4: $ 0 $
Q3: Let $f: \mathbb{C}\setminus { 0, 1 } \rightarrow \mathbb{C}$ be given $f(z) = -\frac{1}{z(z-1)}$. What is the value of the residue $\mathrm{Res}(f, z_0)$?
A1: $1$
A2: $ \frac{1}{2 \pi} $
A3: $ 2 \pi i $
A4: $ 0 $
A5: $ - 1 $
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Last update: 2024-10
