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You may also consider the numeric approximation using N, Total and Table: [mcode]In[1]:= f[max_]:=N[Total[Table[8/(10^n),{n,2,max,2}]],max] In[2]:= f[1000] Out[2]=...
You may want to look into the SaveDefinitions option for Manipulate. Code such as f[x_, a_] := a x^2 Manipulate[Plot[f[x, a], {x, 0, 1}], {a, 0, 10}, SaveDefinitions -> True]will preserve the defiition of f for the manipulate.
Hi, Your system is second order in time and space. Generally, this means you need two spatial boundary conditions and two time conditions.  This is the cause of the first error. Your boundary conditions in the second case are a bit confusing.  y[0,...
This sounds like an issue with the predictive interface. This may be resolved by turning it off. You can read how to do this at     http://support.wolfram.com/kb/11466 Whether that resolves the issue or not, it would help to report this to...