Lecture 14: Non-independent variables
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.
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.
- Transcript of Lesson - Written transcript from this lesson.
- Lecture Notes - Lecture Notes from this lesson.
- Problem Set - A problem set with some problems from this lecture.
- 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?
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Staff Review
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.
