Ordinary Differential Equations 9 | Lipschitz Continuity

[@heisenbergsu5399]

謝謝！

[@brightsideofmaths]

Thanks :)

[@Independent_Man3]

4:35 So L only depends on x and epsilon? Is there a name for functions for which L only depends on \epsilon, like something equivalent to uniform continuity?

[@brightsideofmaths]

I defined a local Lipschitz condition here. Maybe the wikipedia page about Lipschitz continuity can help you about global definitions :)

[@bryangonzalezvallejo7463]

Thanks for the video, what book do you recomend to get more background about this topic?

[@brightsideofmaths]

You can take a look at Ordinary Differential Equations by Wolfgang Walter.

[@johnthicks8568]

I had an OBE while solving ODEs

[@brightsideofmaths]

OMG

[@alexchan4226]

x-y

[@brightsideofmaths]

What do you mean? Is there a mistake?

[@cloudhuang6691]

9:31 excuse me sir, may I ask you why f’ is finite here? The only possible reason I can tell is that we chose epsilon ball of x as a closed ball?

[@brightsideofmaths]

Exactly!

[@cloudhuang6691]

@@brightsideofmaths thank you sir!