Grad of a function in vector notation

In summary, the conversation discusses the computation of the gradient of a function in vector notation and the confusion about the difference between gradient of scalars and vectors. The solution is clarified to be the divergence of q, denoted as ∇.q.
  • #1
leoflindall
41
0

Homework Statement



q = xy[tex]^{2}[/tex]z i + y[tex]^{2}[/tex]xz j + e[tex]^{2z}[/tex] k

Homework Equations



Grad (f) = (fx,fy,fz), where fx, fy, fz are partial derivatives


The Attempt at a Solution



I am Comptent at computing the gradient of a function, however i do not see how to do this when in vector notation. Any Help would be greatly appreciated!

Thank You
 
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  • #2
Hi leoflindall! :smile:

(have a del: ∇ and try using the X2 tag just above the Reply box :wink:)
leoflindall said:
I am Comptent at computing the gradient of a function, however i do not see how to do this when in vector notation. Any Help would be greatly appreciated!

We have gradient of scalars, not of vectors.

Are you sure it isn't .q, the divergence of q ?
 
  • #3
Of course i did, i tihnk it must be the late hour but i was just being silly! Thank you for your help!
 

1. What is "Grad of a function in vector notation"?

"Grad of a function in vector notation" refers to the gradient of a function, which is a vector that shows the direction and magnitude of the steepest increase of the function at a given point.

2. How is the gradient of a function calculated in vector notation?

The gradient of a function can be calculated in vector notation by taking the partial derivatives of the function with respect to each variable and then combining them into a vector.

3. What information does the gradient of a function provide?

The gradient of a function provides information about the direction of the steepest increase of the function at a given point, as well as the rate of change in that direction.

4. How is the gradient of a function used in real-world applications?

The gradient of a function is used in various fields, such as physics, engineering, and economics, to optimize processes and make predictions. It is also used in machine learning algorithms to minimize error and improve accuracy.

5. Can the gradient of a function be negative?

Yes, the gradient of a function can be negative. This indicates a decrease in the function's value in the direction of the gradient. A positive gradient indicates an increase in the function's value in that direction.

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