- #1
calculusisrad
- 20
- 0
Homework Statement
Find a function f(x,y,z) such that F = (gradient of F).
The Attempt at a Solution
I don't know :(
I'm so confused
Please help me!
Calculating Gradients with Vector Calculus
- Thread starter calculusisrad
- Start date
Click For Summary
Homework Help Overview
The discussion revolves around finding a function f(x,y,z) such that F equals the gradient of f, with F given as a vector field. Participants express confusion regarding the problem statement and the nature of gradients in vector calculus.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Some participants question the original problem statement, particularly the notation used for the gradient. Others suggest clarifying whether f or F is provided. There is an exploration of the concept of gradients and the reverse process of differentiation.
Discussion Status
The discussion is ongoing, with participants attempting to clarify the problem and explore potential forms for the function f. Some guidance has been offered regarding the definition of gradients and the differentiation process, but no consensus has been reached.
Contextual Notes
Participants note the urgency of the homework due date and express feelings of being overwhelmed. There is an acknowledgment of the need to show effort in the problem-solving process.
Find a function f(x,y,z) such that F = (gradient of F).
I don't know :(
I'm so confused
Please help me!
- #2
tiny-tim
Science Advisor
Homework Helper
- 25,837
- 258
hi calculusisrad! 
do you mean "Find a function f(x,y,z) such that F = (gradient of f)" ?
(only scalars have gradients, there's no gradient of a vector)
calculusisrad said:
do you mean "Find a function f(x,y,z) such that F = (gradient of f)" ?
(only scalars have gradients, there's no gradient of a vector)
i don't understand either 
is either f or F given in the question?
is either f or F given in the question?
- #3
calculusisrad
- 20
- 0
Sorry, yes you're right. The gradient of f should not be bolded.
- #4
1MileCrash
- 1,338
- 41
Think about what a gradient is. If I told you to find the gradient of a function, what would you do?
You would differentiate the function wrt x, and that is the i component of the gradient, you would differentiate the function wrt y, and that is the j component, and then you would differentiate the function wrt z, and that is the k component.
Now, we are going in reverse. What is the reverse of differentiation?
You would differentiate the function wrt x, and that is the i component of the gradient, you would differentiate the function wrt y, and that is the j component, and then you would differentiate the function wrt z, and that is the k component.
Now, we are going in reverse. What is the reverse of differentiation?
- #5
calculusisrad
- 20
- 0
I completely forgot the biggest part of the problem. WOW. Sorry about that!
Let F = (2xye^z)i + ((e^z)(x^2))j + ((x^2)y(e^z)+(z^2))k
NOW find a function f(x,y,z) such that F = Gradient of f.
Sorry about that. Please answer :)
Let F = (2xye^z)i + ((e^z)(x^2))j + ((x^2)y(e^z)+(z^2))k
NOW find a function f(x,y,z) such that F = Gradient of f.
Sorry about that. Please answer :)
- #6
DivisionByZro
- 250
- 1
"Please answer"? How about you show some effort first? You should have read the forums rules by now.
- #7
calculusisrad
- 20
- 0
This was due last Thursday, I'm horribly behind on homework, I'm desperate here.
- #8
Dick
Science Advisor
Homework Helper
- 26,254
- 623
calculusisrad said:
It's pretty easy to guess a form for f that works. Start guessing. That's often the easiest way to solve problems like this. What's a likely form for f given the first component of F?
Last edited:
- #9
HallsofIvy
Science Advisor
Homework Helper
- 42,895
- 983
You know what the definition of "gradient" is, so use that.
\frac{\partial f}{\partial x}= what?
\frac{\partial f}{\partial y}= what?
\frac{\partial f}{\partial z}= what?
\frac{\partial f}{\partial x}= what?
\frac{\partial f}{\partial y}= what?
\frac{\partial f}{\partial z}= what?
Similar threads
- · Replies 8 ·
- · Replies 1 ·
- · Replies 13 ·
- · Replies 4 ·
- · Replies 4 ·
- · Replies 6 ·
- · Replies 4 ·