-
Title: Lipschitz Continuity
-
Series: Ordinary Differential Equations
-
YouTube-Title: Ordinary Differential Equations 9 | Lipschitz Continuity
-
Bright video: Watch on YouTube
-
Dark video: Watch on YouTube
-
Ad-free video: Watch Vimeo video
-
Forum: Ask a question in Mattermost
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: ode09_sub_eng.srt missing
-
Download bright video: Link on Vimeo
-
Download dark video: Link on Vimeo
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $v: \mathbb{R} \rightarrow \mathbb{R}$ be a locally Lipschitz continuous function. What is not correct in general?
A1: $v$ is continuously differentiable.
A2: $v$ is continuous.
A3: For every point $x \in \mathbb{R}$ there is an $\varepsilon > 0$ and a constant $L > 0$ such that for all points $y,z \in (x- \varepsilon, x+\varepsilon)$, we have $$ |v(y) - v(z) | \leq L | y - z | $$
Q2: Let $v: \mathbb{R} \rightarrow \mathbb{R}$ be given by $v(x) = x^2$. Is $v$ locally Lipschitz continuous?
A1: Yes!
A2: No!
A3: One needs more information.
Q3: Let $v: \mathbb{R} \rightarrow \mathbb{R}$ be given by $v(x) = \sqrt{|x|}$. Is $v$ locally Lipschitz continuous?
A1: No!
A2: Yes
A3: One needs more information.
-
Last update: 2024-10
