To conclude this section, we note that the weak solution u(x;
T) in theo-rem 1 is actually smooth and is a classical solution.
We will not provide the proof of this result, which can be found in [1].
Polynomial time.
Both the addition and multiplication algorithms are considered to be e cient, because their running time grows only mildly with the input length.
More generally, polynomial.
In analysis it is necessary to take limits;
Thus one is naturally led to the construction of the real numbers, a system of numbers containing the rationals and closed under limits.
This differential equation is not separable.
But it is a first order linear dif-ferential equation and by the end of this handout you should be able to solve it.
Evaporation ̈ load the source material-to-be-deposited (evaporant) into the container (crucible) ̈ heat the source to high temperature ̈ source material evaporates ̈ evaporant vapor transports.
When u tiles h or c, this is related to automorphic functions;
And when @u consists of lines or circular arcs, one can also give a di erential equation for f.
We can also de ne analytic.