Explore BrainMass
Share

Gradient Determination of Functions

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Calculate the gradient Vf of the following functions, f(x,y,z)
a. f = x^2 + z^3
b. f = ky where k is a constant
c. f = r = (x^2 + y^2 + z^2)^1/2 Hint use the chain rule
d. f = 1/r

See attachment for better symbol representation

© BrainMass Inc. brainmass.com October 24, 2018, 10:14 pm ad1c9bdddf
https://brainmass.com/physics/scalar-and-vector-operations/gradient-determination-functions-152740

Attachments

Solution Preview

Hello and thank you for posting your question to Brainmass.

The solution is attached below in two files identical in content but differ in format (MS-word and pdf) so you can choose the more suitable one for your needs.

The Del operator is a vector operator. This means that it has three components (in three dimensional space) and it operates on a scalar function:

When applied to a scalar function this ...

Solution Summary

This solution contains step-by-step calculations to determine the gradient of the vector operator using cross product and chain rule.

$2.19
See Also This Related BrainMass Solution

Deriving the PDE for a vector field from its curl and divergence

See Attached

http://farside.ph.utexas.edu/teaching/em/lectures/node37.html

How do they come up with the equations in (308) mathematically? Why do (308) give solutions to (285) and (286). Or why do (308) determine whether (285) and (286) have 1 or more solutions? I don't wonder about the proof for why the La place (309) introduced as a general equation later in the text has only 1 solution. Thanks

View Full Posting Details