Math 222

Homework #5

Instructions. This is due on March 25 at the beginning of class. It is worth 20 points. Late papers lose 3 points per day late. You must work by yourself, but feel free to consult with me. Explain what you did and why you did it: good explanations are essential! Start early, ask questions and do well.

Problems. Do the following for the vector field F(x,y) = < y,x >.

Find a potential function f(x,y).

Find flow lines for F in the equation form g(x,y) = c.

Sketch several flow lines and equipotential curves (f(x,y) = c).

Prove that the flow lines and equipotential curves are orthogonal.

Show that both functions f and g satisfy Laplace's equation u_xx + u_yy = 0.