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August 7th, 2012, 02:11 AM  #1 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  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=Ij. Can anyone help? 
August 7th, 2012, 02:43 AM  #2 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Re: Scalar and vector fields, calculating gradients
Would this be grad f . d ? = 0 
August 7th, 2012, 03:06 AM  #3 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  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.

August 7th, 2012, 03:12 AM  #4 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Re: Scalar and vector fields, calculating gradients
So would this be (2,4) . 1/root 2 (1,1) = 2/root 2 
August 7th, 2012, 03:15 AM  #5 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  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). 
August 7th, 2012, 03:18 AM  #6 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Scalar and vector fields, calculating gradients 
August 8th, 2012, 02:13 AM  #7 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Re: Scalar and vector fields, calculating gradients
Thanks, can you help me with the last 2 parts?

August 9th, 2012, 07:46 AM  #8  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Scalar and vector fields, calculating gradients Quote:
 

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