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August 7th, 2012, 02:11 AM   #1
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Scalar and vector fields, calculating gradients

Hi!

A 2 dimensional scalar field f(x,y)=x^2 -2y^2 +x

I need to find the gradient grad f of the scalar field f and what the value is at point (1,-1).

I have

grad f = (2x)i+(-4y)j

and grad f (1,-1)= 2i+4j

I now need to find the value of the derivative of the scalar field f at the point (1,-1), in the direction of the vector d=I-j.

Can anyone help?
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August 7th, 2012, 02:43 AM   #2
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Re: Scalar and vector fields, calculating gradients

Would this be grad f . d ?

= 0
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August 7th, 2012, 03:06 AM   #3
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Re: Scalar and vector fields, calculating gradients

To be the derivative in the direction of d, it would be , or the dot product of of the gradient of f and the unit vector of d.
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August 7th, 2012, 03:12 AM   #4
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Re: Scalar and vector fields, calculating gradients

So would this be

(2,4) . 1/root 2 (1,-1) = 2/root 2
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August 7th, 2012, 03:15 AM   #5
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Re: Scalar and vector fields, calculating gradients

I also need to find the maximum value of the derivative of the scalar field f at the point (1,-1), and what is its direction is.

And the direction of the tangent line to the contour curve f(x,y) =0 at the point (0,0).
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August 7th, 2012, 03:18 AM   #6
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Re: Scalar and vector fields, calculating gradients

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August 8th, 2012, 02:13 AM   #7
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Re: Scalar and vector fields, calculating gradients

Thanks, can you help me with the last 2 parts?
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August 9th, 2012, 07:46 AM   #8
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Re: Scalar and vector fields, calculating gradients

Quote:
Originally Posted by arron1990
Would this be grad f . d ?

= 0
2- 4 is NOT 0!
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