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Title: Complex Contour Integral
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 18 | Complex Contour Integral
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Bright video: https://youtu.be/qk7gqhuFrj0
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Dark video: https://youtu.be/pA_jfc2RCUM
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ca18_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What is the correct definition for $$ \int_\gamma f(z) , dz $$ if $\gamma: [0,1] \rightarrow \mathbb{C}$ is a parametrized curve?
A1: $ \int_0^1 \gamma(t) dt $
A2: $ \int_0^1 \gamma(t) f^\prime(t) dt $
A3: $ \int_0^1 \gamma^\prime(t) f^\prime(t) dt $
A4: $ \int_0^1 f(\gamma(t)) f^\prime(t) dt $
A5: $ \int_0^1 f(\gamma(t)) \gamma^\prime(t) dt $
A6: $ \int_0^1 f(\gamma^\prime(t)) \gamma dt $
Q2: Let $\gamma: [0,2 \pi] \rightarrow \mathbb{C}$ be given by $\gamma(t) = e^{it}$ and $f(z) = z^2$. What is $ \int_\gamma f(z) , dz $?
A1: $0$
A2: $1$
A3: $2$
A4: $i$
Q3: Let $\gamma: [0,\pi] \rightarrow \mathbb{C}$ be given by $\gamma(t) = e^{it}$ and $f(z) = \overline{z}$. What is $ \int_\gamma f(z) , dz $?
A1: $1$
A2: $\frac{1}{2}$
A3: $\frac{1}{\pi}$
A4: $i \pi $
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Last update: 2024-10
