1 / 4

Chapter 16

Chapter 16. Section 16.8 Differentials. The Differential of The differential of a function of two variables which is denoted is the sum partial derivative with respect to each variable multiplied by the change in the variable for x and for y . It is common to let:.

ronda
Download Presentation

Chapter 16

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 16 Section 16.8 Differentials

  2. The Differential of The differential of a function of two variables which is denoted is the sum partial derivative with respect to each variable multiplied by the change in the variable for x and for y. It is common to let: Differential for : Or, Example Find the differential for The Differential of The differential of a function of two variables which is denoted is the sum partial derivative with respect to each variable multiplied by the change in the variable for x, for y, and for z It is common to let: Differential for : Or, Example Find the differential for

  3. Alternate Notation for the Differential The differential of a function can be expressed in terms of the gradient. It is the gradient dotted with a differential vector: Partial Derivatives of Differential The partial derivatives of the functions that make up a differential when taken with respect to the opposite variable must be equal. If then, but, Contrapositive Just because you have differential combination of x and y does not mean there is a function it is the differential of. If then it is impossible to find a so that, There is no that has the differential form:

  4. Partial Derivatives of Differentials of 3 Variables The partial derivatives of the functions that make up a differential when taken with respect to the opposite variable must be equal even when considering a function of more than two variables. This is seen by considering each pair of functions. If then, but, but, but, If then there does not exist a function such that:

More Related