**Welcome to the Rutgers Maple Help Pages!**

Maple gives you many choices to modify your graphs such as axes, orientation (for 3D graphs), scaling, style, and title. These options can be included in the plot command. For example:

> plot(x^2-sin(x),x=-2..2,axes=frame, scaling=constrained);

Here is a brief overview of the choices for each plot option:

Axes can be FRAME, BOXED, NORMAL, or NONE. Notice the difference in each of the 4 graphs below:

> plot(x^2-sin(x),x=-2..2,axes=frame);

> plot(x^2-sin(x),x=-2..2,axes=boxed);

> plot(x^2-sin(x),x=-2..2,axes=normal);

> plot(x^2-sin(x),x=-2..2,axes=none);

Orientation can be included in 3d graphs. Orientation consists of two angles of the form [theta, phi]. You will learn about these angles when you study spherical coordinates. Orientation is a useful option if you want to look at a graph from a specific angle. Try:

> with(plots);

> plot3d(x^5-y^3,x=-2..2,y=-2..2,orientation=[-91,81]);

versus

> plot3d(x^5-y^3,x=-2..2,y=-2..2);

Notice that in a 3d plot, if you left-click on the graph and hold the mouse button, you can rotate the graph however you like. The angles theta and phi appear in the upper left hand corner of the maple window as you toggle the picture.

The scaling option is unconstrained by default. You can specify scaling=constrained or scaling=unconstrained. Constrained scaling guarantees the same scale will be used on each axis.

The style option changes how Maple draws your graph (with lines or dots, etc.) Style options include style=line, style=point, style=patch, or style=patchnogrid.

You may give your graph a title by adding title="my title" to a plot command.

You will learn about space curves in chapter 13. Maple can graph these easily as follows:

> with(plots):

> spacecurve([cos(t),sin(t),t],t=0..4*Pi,axes=boxed);

Maple can also plot parametric equations in a similar way. Try:

> astr:=[(cos(t))^3,(sin(t))^3,t=0..2*Pi]:

> A:=plot(astr,color=green):

> A;

We saw in the beginning Maple section how to implicitly plot in 2D. When you open the plots package, you can implicitly plot in 3D as well.

To plot more than one 3D graph on the same axes, use the display command. See below:

> with(plots):

> A:=implicitplot3d(x^3+y^3=z^3,x=-5..5,y=-5..5,z=-5..5,color=green,style=patchnogrid):

> B:=plot3d(x^3+y^2,x=-5..5,y=-5..5,color=blue,axes=boxed):

> display({A,B});

Experiment with the commands above. What happens when you change the colon at the end of each of the first 3 lines to a semicolon? Do you see how each part of the A and B commands changes the final graph?

Maple also makes it simple to visualize vector fields using the fieldplot command. To visualize 3D vector field, use the fieldplot3d command.

> with(plots):

fieldplot([x/(x^2+y^2+4)^(1/2),-y/(x^2+y^2+4)^(1/2)],x=-2..2,y=-2..2);

> with(plots):

> fieldplot3d([x/(x^2+y^2+4)^(1/2),-y/(x^2+y^2+4)^(1/2),z],x=-2..2,y=-2..2,z=-2..2,axes=boxed);

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When you open the VectorCalculus package, you can write vectors as follows:

> with(VectorCalculus):

> W:=<2,3,5>;

Your vector need not be numeric though! Try, for example:

> V:=<t^2,t^3,t^4+1>;

You can compute the cross product of vectors V and W in two ways:

> with(VectorCalculus):

> CrossProduct(V,W);

> V &x W;

You can also compute the dot product of V and W in two ways:

> with(VectorCalculus):

> DotProduct(V,W);

> V.W;

> with(VectorCalculus):

> ArcLength(<cos(t),sin(t),t>, 0..6*Pi );

> with(VectorCalculus):

> DirectionalDiff( x^2+y^2, <1,1>, [x,y] );

> with(VectorCalculus):

> Gradient( x^2+y^2, [x,y] );

> with(VectorCalculus):

> TNBFrame(<cos(t),sin(t),t>, t );

Note that this returns a list of 3 vectors: T, then N, then B.

> with(VectorCalculus):

> v:=VectorField(<x,y,z>,'cartesian'[x,y,z]);

> Curl(v);

> Divergence(v);

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> solve({x+y=2,x-y=3},{x,y});

It may happen that you want to solve a more complicated set of equations. For example, try:

> solve({x^2+y^3=2,x-y=3},{x,y});

The result is true, but not numeric. (If you get a solution that includes RootOf, it is a hint that your answer involves complex numbers!) If you would like to see numeric answers, you should try the allvalues command. For example,

> A:= solve({x^2+y^3=2,x-y=3},{x,y}):

> allvalues(A);

Notice that, if possible, allvalues returns all exact (both real and complex!) solutions to the system of equations.

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> with(Student[Calculus1]):

> IntTutor();

A pop-up window should appear. Enter the function you want to integrate in the box at the top of the page. Try different integration rules by pressing the buttons on the right side of the box. If you get stuck, you can ask Maple for a hint.

For practice with derivatives, try

> DiffTutor();

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> ?examples/MultivariateCalculus;

A new Maple worksheet will open with many interesting examples.

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**
Maintained by Last modified 9/5/2006. Address questions to the
Undergraduate Office of the Department of Mathematics.
**