Lecture 14: Non-independent variables

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Taught by OCW
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5166 views | 2 ratings
Lesson Summary:

In this lesson, we learn about finding values when functions have non-independent variables. Specifically, we examine the relationship between variables and how to handle functions that depend on several variables when they're related. We also explore how to find the rates of change of constrained variables with respect to each other, using the example of the area of a right triangle. We clarify the notations used for partial derivatives and emphasize the importance of specifying what is held constant when dealing with related variables.

Lesson Description:

Learn more techniques for finding values when functions have non-independent variables.

Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.

Additional Resources:
Questions answered by this video:
  • How do you find differentials of a function when the variables are not independent?
  • What is the rate of change of the area of a right triangle with respect to theta?
  • If A=1/2absin(theta) and a = bsin(theta), then what is dA/d(theta) for a triangle?
  • Staff Review

    • Currently 4.0/5 Stars.
    This video does a great job of completely explaining several problems dealing with functions with non-independent variables. Several different methods of finding the rate of change of the area of a right triangle with respect to theta, an angle of the triangle are explained. Differentials and the chain rule are given as two systematic methods for finding the solution to these problems.