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Find the divergence of the field.The velocity field $\mathbf{v}(x, y, z)=\left(a^{2}-x^{2}-y^{2}\right) \mathbf{k}$ in Figure 15.14

Calculus 1 / AB

Calculus 3

Chapter 15

Integrals and Vector Fields

Section 8

The Divergence Theorem and a Unified Theory

Integrals

Vectors

Vector Functions

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Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

03:04

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

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Find the divergence of the…

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Find the divergence of $\m…

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all right. So finding the divergence of velocity field we have So we have a partial derivative with respect acts of our I had direction. So we have nothing in our direction. So that's gonna be zero. We have a partial derivative with respect to y and R J had direction, which is also zero. And then we have our partial derivative. With respect to Z in the Kayhan direction, we have to be a squared minus y squared minus X squared. So her first derivative, zero second derivative zero, our third derivative. We have no z's in the K had direction. So the diversions gonna be equal to zero plus zero and then plus our third derivative, which is zero, because we have no please, which is just fall zero.

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