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Title: Multi-Index Notation
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Series: Multivariable Calculus
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YouTube-Title: Multivariable Calculus 15 | Multi-Index Notation
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Bright video: https://youtu.be/Hiwth6HsUq0
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Dark video: https://youtu.be/io-OJAWHAUo
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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: mc15_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: Which of the following objects is not a multi-index by our definition?
A1: $$ \alpha = (-1,1)$$
A2: $$ \alpha = (1,2)$$
A3: $$ \alpha = (2)$$
A4: $$ \alpha = (3,4,5,0,0,0)$$
Q2: Let $\alpha = (0,1,2)$ be a multi-index. What is $\alpha!$ by our definition?
A1: $2$
A2: $1! 2! 3!$
A3: $0$
A4: $1$
A5: $2! 2!$
Q3: Let $\alpha = (0,5)$ be a multi-index. What is $x^{\alpha}$ for $x \in \mathbb{R}^2$?
A1: $x_2^5$
A2: $x_1^5$
A3: $0$
A4: $x_1 x_2^3$
A5: $x_1^2$
Q4: Let $f : \mathbb{R}^2 \rightarrow \mathbb{R}$ be the function given by $f(x_1, x_2) = 2 x_1 x_2^5$ and $\alpha = (1,2)$. What is $D^\alpha f$?
A1: $$ D^\alpha f(x_1, x_2) = 40 x_2^3 $$
A2: $$ D^\alpha f(x_1, x_2) = x_2^3 $$
A3: $$ D^\alpha f(x_1, x_2) = x_1 $$
A4: $$ D^\alpha f(x_1, x_2) = 40 x_1 $$
A4: $$ D^\alpha f(x_1, x_2) = 4 x_1 x_2^4 $$
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Last update: 2024-10
