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Title: Local Diffeomorphisms
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Series: Multivariable Calculus
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YouTube-Title: Multivariable Calculus 22 | Local Diffeomorphisms
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Quiz: Test your knowledge
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Subtitle on GitHub: mc22_sub_eng.srt missing
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Download bright video: Link on Vimeo
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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: Is following map a diffeomorphism? $$ \Phi: (0,\infty) \times \mathbb{R} \rightarrow \mathbb{R}^2 \setminus { 0 } , , ,,, (r, \varphi) \mapsto \begin{pmatrix} r \cos(\varphi) \ r \sin(\varphi) \end{pmatrix} $$
A1: No, because $f$ is not injective.
A2: No, because $f$ is not surjective.
A3: Yes!
A4: No, because $f$ is not differentiable.
Q2: Is following map a diffeomorphism? $$ \Phi: (0,1) \times (0,\pi) \rightarrow \mathbb{R}^2 \setminus { 0 } , , ,,, (r, \varphi) \mapsto \begin{pmatrix} r \sin(\varphi) \ r \cos(\varphi) \end{pmatrix} $$
A1: No, because $f$ is not injective.
A2: No, because $f$ is not surjective.
A3: Yes!
A4: No, because $f$ is not differentiable.
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Last update: 2024-10
