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).
Average Rate of Change Examples
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
Intro to a Variable as a Changing Value or Placeholder
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
Introduction to Time Rate of Change (Differential Equations 5)
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
Change of variables and the integral -- Calculus I
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
Calculus - What is a Derivative? (6 of 8) How Fast Is The Dependent Variable Changing?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how fast the dependent variable changing when the independent variable changes.
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
Worldwide Calculus: Change of Coordinates
Lecture on 'Change of Coordinates' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Direct Linear Variation (1 of 2: Introduction)
More resources available at www.misterwootube.com
From playlist Further Ratios and Rates
Ex: Determine Percent of Change - Increase and Decrease
This video provides 4 examples of how to determine the percent of change.
From playlist Percent of Change
Turn graphic data into algebraic equations.
From playlist Algebra: Linear Equations with One Variable
CSS Variables / Custom Properties (full course)
CSS Custom Properties (aka Variables) bring the power of variables to CSS, which results in less repetition, better readability and more flexibility. Originally posted on Scrimba: https://scrimba.com/g/gcssvariables When viewing the Scrimba version of this course, you can pause the video
From playlist Full Courses in One Video
Setting Variables with Levels of Measurement: Discover Statistics with JASP for Beginners (3 of 6)
Each variable in JASP is assigned a level of measurement (nominal, nominal text, ordinal, or scale). We learn how to change or set those levels and how to set and adjust value levels for categorical variables. I cover whether we have to set levels and how setting levels benefits us. This i
From playlist Discovering Statistics with JASP
RubyConf 2021 - Improving CVAR performance in Ruby 3.1 by Eileen M Uchitelle
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
Changing Variables and Other Calculus Tools
In recent versions, we have added functionality to make Wolfram Language more directly applicable to the calculus classroom. I will focus, in particular, on the new functions ImplicitD, IntegrateChangeVariables and DSolveChangeVariables. Other related enhancements will be covered as time p
From playlist Wolfram Technology Conference 2022
Mod-12 Lec-26 Cost Volume Profit Analysis
Managerial Accounting by Dr. Varadraj Bapat,Department of Management,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Managerial Accounting | CosmoLearning.org Accounting
The Multi-Variable Chain Rule: Derivatives of Compositions
Suppose that f(x,y) depends on two variables but that the x(t) and y(t) are themselves both functions of t. Then f(x(t), y(t)) is a composition of functions and the derivative of f with respect to t is computed via the multi-variable Chain Rule. In fact, this scenario is one of many differ
🔥Learn JavaScript in 12 hours | JavaScript Tutorial For Beginners | JavaScript 2022 | Simplilearn
🔥FREE JavaScript Course With Completion Certificate: https://www.simplilearn.com/learn-javascript-basics-free-course-skillup?utm_campaign=JS12hrs16oct22&utm_medium=DescriptionFirstFold&utm_source=youtube Learn JavaScript in 12 hours video by simplilearn on Learn JavaScript is a complete f
From playlist Simplilearn Live
Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007
Lecture 11: Differentials; chain rule. View the complete course at: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.02 Multivariable Calculus, Fall 2007
Ex: Find the Average Rate of Change Given a Function on [2,t]
This video explains how to find the average rate of change of a function on an interval containing a variable. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Average Rate of Change
Linear Programming. Lecture 21. Change the objective function; Adding a new variable.
November 8, 2016. Penn State University.
From playlist Math484, Linear Programming, fall 2016