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rammer

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What's the algorithm for finding scalar function satisfying div f=F if I know vector F?

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In summary, the algorithm for finding a scalar function satisfying grad f=F is to use the concept of potential functions, as shown in the provided link. This allows for the conversion of a vector field into a scalar function, such as in the case of finding electric potential from electric intensity.

- #1

rammer

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What's the algorithm for finding scalar function satisfying div f=F if I know vector F?

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- #3

rammer

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rammer said:

Look at the following link for an example:

http://www.math.wisc.edu/~conrad/f07/potentials.pdf

- #5

rammer

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thanks, that's exactly what i was looking for

A scalar function is a mathematical function that takes a single input variable and produces a single output value. It is used to describe a physical quantity that has only magnitude, such as temperature or pressure.

In mathematical terms, a scalar function satisfies div f=F if its divergence (div f) is equal to the given scalar field F. This means that the rate of flow of the function at a given point is equal to the value of the scalar field at that point.

A scalar function can be used to describe a component of a vector field, such as its magnitude or direction. In fact, a vector field can be decomposed into scalar functions, with each scalar function representing a different component of the vector field.

When a scalar function satisfies div f=F, it means that the function follows a specific mathematical relationship with the scalar field. This can provide useful information about the behavior and properties of the function and how it relates to the scalar field.

The concept of a scalar function satisfying div f=F is used in many areas of science and engineering, such as fluid mechanics, electromagnetics, and heat transfer. It allows for the analysis and modeling of physical phenomena involving both scalar fields and vector fields.

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