## Math 273 Computer Tools

The computer tool Maple is available online from the Math Department MyMath Math Portal; after login just follow the "Software" link. Some tutorial information about Maple is given at this Maple tutorial website, and there is also online Maple help within the MyMath Maple environment. Here are some example Maple commands for working with multivariable calculus.

• Plot the cylinder 2y^2 = z + 1:
with(plots): eq := 2*y^2 = z+1;
implicitplot3d(eq,x=-2..2,y=-2..2,z=-2..2,axes=framed);
You can rotate the plot by adding orientation parameters, e.g. try
implicitplot3d(eq,x=-2..2,y=-2..2,z=-2..2,axes=framed,orientation=[135,45]);
the default corresponds to orientation=[45,45];
• Plot the surface 2y^2 = x^2 - 2z^2 + 1:
with(plots): eq := 2*y^2 = x^2-2*z^2+1;
implicitplot3d(eq,x=-2..2,y=-2..2,z=-2..2,axes=framed);
• Plot the two surfaces y = x^2 + 2z^2 and y = 2 - 3z^2 on the same graph:
with(plots): eq1 := y = x^2+2*z^2; eq2 := y = 2-3*z^2;
implicitplot3d({eq1,eq2},x =-2..2,y =-1..3,z =-2..2,axes=framed);
• Plot the curve r(t)= &lang sin(t), 3cos(t), t &rang for 0 &le t &le 2&pi and determine its arc length :
with(plots):
r := [sin(t),3*cos(t),t];
v := diff( r, 't' );
spacecurve(r(t),t=0..2*Pi,axes=framed);
with(linalg): rv := sqrt(dotprod(v,v));
L := evalf( int( rv, t=0..2*Pi ) );
Determine the curvature:
with(VectorCalculus):
Curvature( < sin(t), 3*cos(t), t > );
• Determine the graph and the contour plot for f(x,y)=4x^2 + 2(y-1)^2 - 1:
with(plots): f := 4*x^2 + 2*(y-1)^2 - 1;
plot3d( f, x = -4..4, y = -3..5, axes=framed );
contourplot( f, x = -4..4, y = -3..5, axes=framed );
contourplot3d( f, x = -4..4, y = -3..5, axes=framed );
• Plot the 2-d vector field &lang y, sin(x) &rang:
with(plots): fld := [ y, sin(x) ];
fieldplot( fld, x=-1..1, y=-1..1, grid=[8,8] );
• Plot the 3-d vector field &lang x, y, z &rang/|&lang x, y, z &rang|:
with(plots): r := sqrt(x^2 + y^2 + z^2); fld := [ x/r, y/r, z/r ];
fieldplot3d( fld, x=0..1, y=0..1, z=0..1, grid=[8,8,8] );
• Plot the surface in 3-d defined by r(u,v) = &lang u^2+1, v^2+1, u+v &rang for -1 &le u &le 1, -1 &le v &le 1:
S := [u^2 + 1, v^2 + 1, u+v];
plot3d(S,u=-1..1,v=-1..1,axes=framed);