Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

How would you show that a given vector field in $ℝ^{2}$ is not conservative?

A given vector field in $ℝ^{2}$ is not conservative when, $F (x, y) \neq \nabla f (x, y) \neq \frac{\partial f}{\partial x} i + \frac{\partial f}{\partial y} j$

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TABLE OF CONTENTS

Step 1.Given Information

How would you show that a given vector field in $ℝ^{2}$ is not conservative?

Step 2. A vector field is conservative

If a vector field can be described as a gradient, it offers a number of mathematically appealing properties, including the ability to be easily integrated along curves. Such fields are referred to as conservative vector fields.

A vector field that is conservative. F is a vector field that represents the gradient of a function $f$ .

Step 3. A conservative vector field F is a vector field that can be written as the gradient of some function f.

That is,

$F (x, y) = \nabla f (x, y) = \frac{\partial f}{\partial x} i + \frac{\partial f}{\partial y} j$

Hence, we can say that a given vector field in $ℝ^{2}$ is not conservative, when

$F (x, y) \neq \nabla f (x, y) \neq \frac{\partial f}{\partial x} i + \frac{\partial f}{\partial y} j$

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Calculus

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Short Answer

How would you show that a given vector field in $ℝ^{2}$ is not conservative?

Step by Step Solution

Step 1.Given Information

Step 2. A vector field is conservative

Step 3. A conservative vector field F is a vector field that can be written as the gradient of some function f.

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Short Answer

How would you show that a given vector field in ℝ2 is not conservative?

Step by Step Solution

Step 1.Given Information

Step 2. A vector field is conservative

Step 3. A conservative vector field F is a vector field that can be written as the gradient of some function f.

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How would you show that a given vector field in $ℝ^{2}$ is not conservative?