/sci/ - Science & Math

>>9769823
Because solutions have to exist before you can solve it, whether through analytical methods or numerical methods.
Also numerical methods have problem with non-[math]C^1[/math] boundary conditions since they can't chop up the domain into infinitely many small pieces (hence the name [math]finite[/math] element).
>>9769826
PDE's are beautiful geometric optimization problems while ODE's are monstrocities (at the research level). E.g. Atiyah-Singer sindex theorem in PDE's vs. the Airy equation having non-[math]L^2[/math] solutions in ODE.
>>9769828
>mfw an undergrad answers questions he's not equipped to answer