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Title: Isolated Singularities
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 16 | Isolated Singularities
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Bright video: https://youtu.be/4LzhMll8O8U
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Dark video: https://youtu.be/KRUn7WuWzfY
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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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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ca16_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 $$f(z) = \sum_{k=-\infty}^\infty a_k z^k$$ be a Laurent series where $a_k = 0$ for all $k<-3$ and $a_{-3} = 1$. Which statement is correct?
A1: $f$ has a pole at $-3$.
A2: $f$ has a pole of order $0$ at $-3$.
A3: $f$ has a pole at $0$ of order $-3$.
A4: $f$ has a pole of order $3$ at $0$.
A5: $f$ has a pole of order $3$ at $1$.
Q2: Let $f(z) = z^2 + \frac{1}{z^3}$. Does $f$ has pole at $0$?
A1: Yes, it’s of order $1$.
A2: Yes, it’s of order $2$.
A3: Yes, it’s of order $3$.
A4: No!
Q3: Which is not a type of an isolated singularity?
A1: removable singularity
A2: linear singularity
A3: essential singularity
A4: pole
Q4: Does $\cos(z^{-1})$ have an isolated singularity at $0$?
A1: Yes, but it’s removable.
A2: Yes, it’s a pole.
A3: Yes, it’s an essential singularity.
A4: No!
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Last update: 2024-10
