Math 241H, section 0101, Fall 2005 Matlab 4 Matlab is very good at ...

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Math 241H, section 0101, Fall 2005 Matlab 4 Matlab is very good at plotting vector fields both in two and three di- mensions. Ad

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Math 241H, section 0101, Fall 2005 Matlab 4 Matlab is very good at plotting vector fields both in two and three di- mensions. Additionally, using vector fields it can be easy to approximate divergence and curl for certain points, and to see the sign of a line integral. The quiver command easily displays vector fields in two dimensions. Suppose the vector field is given by F(x, y) = u(x, y)i + v(x, y)j. The func- tions u and v can be written as mfiles or inline. We then need to con- struct a mesh [X, Y ] as done before and finally the command is given by quiver(X,Y,u(X, Y ),v(X, Y )). One warning is to not make the mesh too fine, put on too many arrows, about 5-20 divisions in each direction is a good rule of thumb. Suppose F(x, y) = xi + (x2 + y2)j over the rectangle [?2,2] × [?2,2]. To have matlab plot the vector field enter the following: >> u=inline(’x’,’x’,’y’) >> v=inline(’x.^2 + y.^2’,’x’,’y’) >> x=linspace(-2,2,11); >> y=linspace(-2,2,11); >> [X,Y]=meshgrid(x,y); >> U=u(X,Y); V=v(X,Y); >> quiver (X,Y,U,V) >> axis image (this last command sets the tick marks) Sometimes we want to see a unit vector field. To adjust the vector field we make sure that each vector is a unit. To do this enter the the following in place of the last three lines above. >> U1=U./sqrt(U.^2 + V.^2); V1=V./sqrt(U.^2 + V.^2); >> quiver (X,Y,U1,V1) >> axis image To graph a vector field in three dimensions use the command quiver3. For instance, to graph the vector field F(x, y, z) = yi+xj+(x2 +z)k over the

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