Vector calculus. Divergent vector field.

In summary, the conversation suggests that the person is having trouble with a specific problem related to gradients and divergences. The solution is to take the gradient of f to get a vector field, then apply div to that vector field to find the answer. Additionally, the person agrees with the advice to first find the gradient of f and then the divergence.
  • #1
carstensentyl
34
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I don't even know where to start this one. I can do all the other problems in the section, but this one makes no sense
 
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  • #2
a). since you've done the other problems, you surely saw some gradients and divergences. The easiest way to do this is piece by piece. First take the gradient of f to get a vector field. Then simply apply div to this vector field to get the answer.

once you get this you will see the answer for part b
 
  • #3
um just do what it says? what part are you having trouble with?
 
  • #4
I agree with ice109- if the problem asks you to find "div grad f", I would recommend that you first find the grad of f and then the div of that! I am assuming that, since you were given a problem like this, you know what "div" and "grad" are.
 

1. What is vector calculus?

Vector calculus is a branch of mathematics that deals with the differentiation and integration of vector fields. It combines the concepts of multivariable calculus, linear algebra, and geometry to study and analyze the properties of vector fields.

2. What is a vector field?

A vector field is a mathematical function that assigns a vector to each point in a given space. This vector represents the direction and magnitude of a physical quantity, such as velocity, force, or electric field, at that point.

3. What is divergence?

Divergence is a measure of how much a vector field is "spreading out" or "converging" at a given point. It is represented by the divergence operator (∇ · F) and is a scalar value. A positive divergence indicates that the vectors are spreading out, while a negative divergence indicates they are converging.

4. What is a divergent vector field?

A divergent vector field is a vector field in which the vectors are spreading out from a given point. This means that the divergence at that point is positive. Examples of divergent vector fields include a source, where vectors radiate outwards, and a fluid flow, where particles move away from a center point.

5. How is divergence used in vector calculus?

Divergence is an important concept in vector calculus as it helps us understand and analyze the behavior of vector fields. It allows us to determine whether a vector field is converging or diverging at a given point, and can be used to solve a variety of physical and mathematical problems, such as calculating fluid flow rates or finding electric field strengths.

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