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Unformatted text preview: Mathematics 20E - Spring 2009 - Homework 2 April 13, 2009 Please complete the following problems and turn them in to the homework drop box in the sixth floor of AP&M labelled “Math 20E / Ryan Szypowski” by Friday, April 24 at 5:30pm. Only a subset of the problems will be graded; leave some blank at your own risk. 1. Let f : Ê 2 → Ê be given by f ( x, y ) = x + y. Sketch the vector field given by F = ∇ f and show that c ( t ) = parenleftbigg x y parenrightbigg + t parenleftbigg 1 1 parenrightbigg is a description of the flow line of this field through the point ( x , y ). 2. Let g : Ê 2 → Ê be given by g ( x, y ) = xy. Sketch the vector field given by G = ∇ g and show that d ( t ) = 1 2 parenleftbigg ( x + y ) e t + ( x − y ) e- t ( x + y ) e t − ( x − y ) e- t parenrightbigg is a description of the flow line of this field through the point ( x , y ). 3. Let F ( x, y, z ) = ( x + y + z )( i + 2 j + k ) ....
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- Vector Space, 2J, Vector field, Ryan Szypowski