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
Famous quotes containing the words change of, change and/or variables:
“The change of Philomel, by the barbarous king
So rudely forced: yet there the nightingale
Filled all the desert with inviolable voice
And still she cried, and still the world pursues,
“Jug Jug” to dirty ears.”
—T.S. (Thomas Stearns)
“The change of Philomel, by the barbarous king
So rudely forced; yet there the nightingale
Filled all the desert with inviolable voice
And still she cried, and still the world pursues,
“Jug Jug” to dirty ears.”
—T.S. (Thomas Stearns)
“The variables are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.”
—George Steiner (b. 1929)