Answer: Gradient fields Find the gradient field F = for

Chapter 14, Problem 27E

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QUESTION:

Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the potential function \(\varphi\). Sketch a few level curves of \(\varphi\) and a few vectors of F.

\(\varphi(x, y)=\sin x \sin y, \text { for }|x| \leq \pi,|y| \leq \pi\)

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QUESTION:

Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the potential function \(\varphi\). Sketch a few level curves of \(\varphi\) and a few vectors of F.

\(\varphi(x, y)=\sin x \sin y, \text { for }|x| \leq \pi,|y| \leq \pi\)

ANSWER:

Solution 27E

Step 1

For a function of the form, the gradient of the function is given as follows:

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