Definition talk:Stability (Differential Equations)
This page references a lot of terms which need definitions, and links to them.
I also believe that:
- $||x - x_0|| < \delta \Rightarrow ||\phi(t,x) - \phi(t,x_0)|| < \epsilon$
should perhaps be rendered:
- $|x - x_0| < \delta \Rightarrow |\phi(t,x) - \phi(t,x_0)| < \epsilon$
i.e. the notation defining "absolute value" not "norm" - if it's the latter then I don't understand what it means and it needs to be explained. --Prime.mover 20:40, 20 April 2010 (UTC)
I think the problem is I don't like boldfacing my vectors. I haven't done that in a few years, and we didn't even use that in my lin alg, diff eq, or multivar calc classes. Colors
In that case we may have a problem. The symbology you are using is sufficiently non-standard as to need to be explained. If you have neither the time nor the patience to use a notation that indicates that a particular quantity is of a standard type (in this case, a vector, I presume??) then it might be a good idea to put a note somewhere indicating what they are. As it stands, none of the variables on this page have any indication that they are vectors.
I steered clear of much of linear algebra and multivariate calculus beyond learning the very basics, so my knowledge of this field is rusty. However, it would be good if we were able to provide sufficient background so as to at least define the terms used in terms of other simpler ones. As it stands, there are one or two concepts on this page that can be guessed, a couple of others which have the basics of a definition already in existence on ProofWiki, and a few others which need a proper definition page set up before the reader has a hope of understanding.
As I say, I don't understand this page as it stands. This is not my fault. --Prime.mover 09:46, 25 April 2010 (UTC)