Elementary algebra

Change of variables

In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem. Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation (chain rule) or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial: Sixth-degree polynomial equations are generally impossible to solve in terms of radicals (see Abel–Ruffini theorem). This particular equation, however, may be written (this is a simple case of a polynomial decomposition). Thus the equation may be simplified by defining a new variable . Substituting x by into the polynomial gives which is just a quadratic equation with the two solutions: The solutions in terms of the original variable are obtained by substituting x3 back in for u, which gives Then, assuming that one is interested only in real solutions, the solutions of the original equation are (Wikipedia).

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In this video we see two examples of word problems involving the average rate of change. Remember the average rate of change formula: (f(b) - f(a))/(b-a)

From playlist Calculus

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This video defines a variable and provides examples of a variable used as a changing value or a placeholder http://mathispower4u.com

From playlist Algebraic Structures Module

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https://www.patreon.com/ProfessorLeonard An explanation of Time Rate of Change and how it is a basic Differential Equation where time is our independent variable.

From playlist Differential Equations

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This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus I

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From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?

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From playlist Multivariable Derivatives

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From playlist Further Ratios and Rates

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This video provides 4 examples of how to determine the percent of change.

From playlist Percent of Change

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From playlist Algebra: Linear Equations with One Variable

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From playlist Full Courses in One Video

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From playlist Discovering Statistics with JASP

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Have you ever wondered how class variables (CVARs) in Ruby work? Would you be surprised to learn that their performance becomes increasingly worse as the inheritance chain grows? I’m excited to share that in Ruby 3.1 we fixed the performance of CVARs. In this talk we'll look at the langua

From playlist RubyConf 2021

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From playlist Calculus III: Multivariable Calculus (Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization, etc) **Full Course **

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From playlist MIT 18.02 Multivariable Calculus, Fall 2007

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Ex: Find the Average Rate of Change Given a Function on [2,t]

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From playlist Average Rate of Change

Related pages

Jacobian matrix and determinant | Derivative | Chain rule | Probability density function | Polynomial decomposition | Boundary value problem | Variable (mathematics) | Abel–Ruffini theorem | Expression (mathematics) | Substitution (algebra) | Universal instantiation | Function (mathematics) | Diffeomorphism | Real number | Integral | Calculus | Analytic function | Integration by substitution | Change of variables (PDE) | Pressure gradient | Isaac Newton | Quadratic equation