Changes

'''Changing variables''' is a mathematical practice used to put equations into more convenient forms by substituting certain variables for expressions which they are equal to.  For example, if <tt>x=y+1</tt>, the expression <tt>z=5(y+1)</tt> could be rewritten <tt>z=5x</tt>.  Change of variables is never absolutely necessary, but it can greatly simplify problems and help avoid errors.  While most frequently used in [[integration]], it can also be helpful to a lesser degree in algebra.

'''Changing variables''' is a mathematical practice used to put equations into more convenient forms by substituting certain variables for expressions which they are equal to.  For example, if <tt>x=y+1</tt>, the expression <tt>z=5(y+1)</tt> could be rewritten <tt>z=5x</tt>.  Change of variables is never absolutely necessary, but it can greatly simplify problems and help avoid errors.  While most frequently used in [[integration]], it can also be helpful to a lesser degree in [[algebra]].

A change of variables transforms the original plain into another.  Areas and lengths are transformed in a uniform ratio, allowing one to solve problems in the second plain and then transform the areas back to the original plane.  For example, when one defines <tt>u=x²</tt> and <tt>v=1/x</tt>, the x-y plane is transformed into the u-v plane.

A change of variables transforms the original plain into another.  Areas and lengths are transformed in a uniform ratio, allowing one to solve problems in the second plain and then transform the areas back to the original plane.  For example, when one defines <tt>u=x²</tt> and <tt>v=1/x</tt>, the x-y plane is transformed into the u-v plane.