In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way. The intent is that the problem expressed in new variables may be simpler, or equivalent to a better understood problem.
A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth order polynomial:
Sixth order polynomial equations are generally impossible to solve in terms of elementary functions. This particular equation, however, may be simplified by defining a new variable x3 = u. Substituting this into the polynomial:
which is just a quadratic equation with solutions:
The solution in terms of the original variable is obtained by replacing the original variable:
Read more about Change Of Variables: Differentiation, Integration, Differential Equations
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