= Forced Airy boundary-value problem
{title2=$-u''+xu=f,\quad u(0)=u(1)=0$}
On the unit interval, the weak form is $a(u,v)=\int_0^1fv$, with $a(u,v)=\int_0^1(u'v'+xuv)$ on the <zero-boundary Sobolev space>. The nonnegative potential makes this form coercive in the derivative <norm>, and the <Poincaré inequality> makes that <norm> equivalent to the <Sobolev norm>. The <Lax-Milgram theorem> gives a unique solution. A conforming <Ritz method> minimizes the corresponding strictly convex quadratic energy and produces a symmetric positive-definite <tridiagonal> <matrix> for piecewise-linear hats.
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