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 and/or variables:
“Parents who expect change in themselves as well as in their children, who accept it and find in it the joy as well as the pains of growth, are likely to be the happiest and most confident parents.”
—Fred Rogers (20th century)
“The variables of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)