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- Change_of_variables abstract "In mathematics, the operation of substitution consists in replacing all the occurrences of a free variables appearing in an expression or a formula by a number or another expression. In other words, an expression involving free variables may be considered as defining a function, and substituting values to the variables in the expression is equivalent to apply the function defined by the expression to these values.A change of variables is commonly a particular type of substitution, where the substituted values are expressions depending of other variables. This is a standard technique used to reduce a difficult problem to a simpler one. A change of coordinates is a common type of change of variables. However, if the expression in which the variables are changed involves derivatives or integrals, the change of variable does not reduce to a substitution.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 radicals (see Abel–Ruffini theorem). This particular equation, however, may be simplified by defining a new variable x3 = u. Substituting x by into the polynomial giveswhich is just a quadratic equation with solutions:The solution in terms of the original variable is obtained by substituting back u by x3 in this solution:".
- Change_of_variables wikiPageID "2146848".
- Change_of_variables wikiPageRevisionID "605430190".
- Change_of_variables hasPhotoCollection Change_of_variables.
- Change_of_variables subject Category:Elementary_algebra.
- Change_of_variables subject Category:Mathematical_physics.
- Change_of_variables comment "In mathematics, the operation of substitution consists in replacing all the occurrences of a free variables appearing in an expression or a formula by a number or another expression.".
- Change_of_variables label "Change of variables".
- Change_of_variables label "Substitutie (wiskunde)".
- Change_of_variables label "Substitution (Mathematik)".
- Change_of_variables label "Подстановка".
- Change_of_variables sameAs Substituce_(matematika).
- Change_of_variables sameAs Substitution_(Mathematik).
- Change_of_variables sameAs Substitutie_(wiskunde).
- Change_of_variables sameAs m.05fc5nf.
- Change_of_variables sameAs Q1934165.
- Change_of_variables sameAs Q1934165.
- Change_of_variables wasDerivedFrom Change_of_variables?oldid=605430190.
- Change_of_variables isPrimaryTopicOf Change_of_variables.