{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2220hw9

# 2220hw9 - Math 2220 Section 3.3 Problem Set 9 Spring 2010 1...

This preview shows page 1. Sign up to view the full content.

Math 2220 Problem Set 9 Spring 2010 Section 3.3 : 1. For the vector field F ( x,y ) = ( x,y ) do the following things: (a) Sketch the vector field. (b) Determine the flow lines by solving the differential equations dx dt = x and dy dt = y . Your answer should be functions x ( t ) and y ( t ) each of which depends on an arbitrary constant. (c) Check that the flow lines are hyperbolas by eliminating the variable t from your formulas in part (b). (d) Find the values of the arbitrary constants that give the flow line c ( t ) such that c (0) = (2 , 1). 2. Sketch the vector field F ( x,y ) = ( x,x 2 ), determine the flow lines, and show the flow lines are parabolas. 3. Verify that the parametrized curve c ( t ) = (sin t, cos t, 2 t ) is a flow line for the vector field F ( x,y,z ) = ( y, x, 2). 4. Consider the vector field F ( x,y ) = (2 x, 3). (a) Find a function f ( x,y ) whose gradient vector field is equal to F , so F = f . (b) Determine the equipotential curves of F (in other words, the level curves of f ). Sketch a couple of these curves, and sketch what the vector field
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online