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Title: Application of the Residue Theorem
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 35 | Application of the Residue Theorem
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Bright video: https://youtu.be/t0Pp3460hoE
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Dark video: https://youtu.be/jqOtm-WfT4A
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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: ca35_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: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = \frac{1}{1+x^2}$. Does the improper Riemann integral $$ \int_{-\infty}^{\infty} f(x) , dx$$ exist?
A1: Yes!
A2: No!
A3: One needs more information.
Q2: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = \frac{1}{1+x^2}$. Let’s calculate the integral $$ \int_{-\infty}^{\infty} f(x) , dx$$ like shown in the video. Which isolated singularity do we need for that?
A1: $i$
A2: $-i$
A3: $1$
A4: $-1$
A5: $0$
Q3: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = \frac{1}{1+x^2}$. Let’s calculate the integral $$ \int_{-\infty}^{\infty} f(x) , dx$$ like shown in the video. What is the value of this integral?
A1: $ 2 \pi i \cdot \frac{1}{2 i} = \pi $
A2: $ 2 \pi i \cdot 0 = 0 $
A3: $ 2 \pi i \cdot \frac{1}{i} = 2 \pi $
A4: $ 2 \pi i \cdot \frac{1}{2} = i \pi $
A5: $ \pi i \cdot \frac{1}{2 i} = \frac{\pi}{2} $
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Last update: 2024-10
