MathGroup Archive 2005

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Re: Partial diff equations


You are expecting too much.  At the moment (perhaps things will be
different in 2100) computer algebra systems can help humans do
mathematics as tools, but cannot carry out any deep developments on
their own.  Its the difference between (a+b)^2=a^2+2ab+b^2 and FLT.

PDEs is one area where only humans can go deep because there are no
general solution methods, only some generic rules (Greens functions,
domain of validity, etc). Few can be solved in closed form for
arbitrary boundary or initial conditions.  I noticed that your example
has no specified domain or BCs. It is a particular solution.

On the other hand, many ODE classes are amenable to general solution
procedures, e.g. using Laplace or Fourier transforms, so they can be
put in a rule database, just like integrals.


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