functional-analysissoft-questionterminology
Hope this is not a stupid "what is X" question.
I read a book from applied mathematics and I failed to find any reference for the concept "conserved". I am not sure if this is a mathematical jargon or if there is a definition for it.
What does it mean when one says that "the $L^2$-norm of $u$ is conserved"?
It is true that the meaning of trivial varies as the complexity of the subject increases, or when the area of expertise of the writer is not yours. I find some stuff trivial, which might not be trivial for another person. Even with expert mathematicians, something might be trivial for a number theorist which might not really be trivial for a topologist, for example.
When you find trivial in a book it usually means: "This should be rather easy to see for anyone that has got this far into the theory", or "I think this is easy to see and I don't want to waste my time in proving it", among others. I really suggest you take a look at JM's link, since it has great answers and it is almost the same situation.
Since most of book covers on research mathematics is intentionally kept sober, to make a poster you may want to keep it simple yet not too boring. Also, it depends on the subject, audience, medium and budget.
Some tips:
keep it simple or to borrow the term: minimalistic
Visual wordplay or pun (as long as it is not overdone) OR, allusion to artwork such as Magritte or Escher if you are dealing with a topic that is self-referential, but avoid being cliche. Since mathematics is hotbed for symbols and logos, you can alter the font to mold into an object. The zero-sharp, zero-dagger, club suit, diamond suit, etc. Example, a bird morphing from "w" (the smallercase Greek omega letter)
You can also use an equation in a Rebus style such as the much abused meme of $i$, complex number and irrationality. Although memes can be rather cheap humor, you can browse to keep ideas flowing. This cartoon was quite interesting. (It can also be a simple Euler's identity with the tagline: Thus God exists.) Also, try to make a campaign - to borrow advertising term- so that you keep one constraint, eg: Thus God exist and you show mathematical equations such as the the one already mentioned, Kurt Goedel's proof, etcetera. Only caveat: keep it simple and connect in a non-sequiter manner. If you show the image of two balls from one of Banach-Tarski paradox, your tagline could be something of the nature such as: Never a boring day at the classroom.
Probably a historical image in a monotone shade either a sketch of the mathematician if he is obscure or of the university or locale
Keep in mind of that if it is posted on a bullet inboard, passerby will have very short span to notice it, so it cannot be too deep to "get it"
Another idea could be "ambient"-a term in advertising, where you use the surrounding to prove a point, such as a life-size ballerina image around revolving door. Stickers on calendars, numpad on phone, mirror, trees can be ways to spread the message. Taglines like: Average person sees a tree, a number theorist sees the sequence: 1 1 2 3 5... or, Average person sees an coffee, but a topologist sees a a donut. (The last one is cliche, but for illustration purpose).
Some examples:
The famous book cover wittily shows and tells the theme
A Cantor one I found online that shows but does not tell the theme
Best Answer
It would be useful if you'd provide more context, as the precise meaning varies from case to case. In general, the term "conserved" occurs when you are studying something which is being changed, yet some property of the thing remains the same. We then say that this property is "conserved".
In your case, I'd guess that you have some transformation $t$ acting on $u$, in which case "the $L^2$-norm of $u$ is conserved" means that the $L^2$-norm of $t(u)$ is the same as the $L^2$-norm of $u$.