<\body> The center value for the Godunov scheme is (supposing Riemann ICs at =0>) <\equation*> u>(x,t)=>|s*,>>|>|s*,>>>>>>|\u,>>|>|f(u),>>|)(0)>|(u)\0\f(u)>>|>|(u)\0,>>>>>>|\u>>>>> with <\equation*> s\)-f(u)|u-u> according to my own calculation. We can simplify some more, to get <\equation*> >|)\f(u)*,>>|>|)\f(u),>>>>>>|\u,>>|>|f(u),>>|)(0)>|(u)\0\f(u)>>|>|(u)\0,>>>>>>|\u.>>>>> This yields <\eqnarray*> >||>(x))>>|||)>|)\f(u)*,>>|)>|)\f(u),>>>>>>|\u,>>|)>|f(u),>>|)(0)>|(u)\0\f(u)>>|)>|(u)\0,>>>>>>|\u>>>>>>>|||[u,u]>f(u)>|\u,>>|)>|f(u),>>|[u,u]> f(u)>|(u)\0\f(u)>>|)>|(u)\0,>>>>>>|\u>>>>>>>|||[u,u]>f(u)>|\u,>>|[u,u]> f(u)>|\u>>>>>>>>> which is just what's in the notes, thus verifying the claimed value >> for the Godunov scheme.