# Maple Information

1. Commands end with a colon (:) or a semicolon (;). Most of the time, you will end with a semicolon. The difference between the two is that a colon suppresses the output (for example, if you don't want to see the result of an intermediate calculation), while the semicolon displays the output. Try both 2+2: and 2+2; in your MAPLE window sometime.
2. Many basic commands are loaded automatically when you start MAPLE. However, many others are not and must be loaded explicitly before you can access the commands. The commands are organized into packages. We will want the following packages loaded most of the time: plots (a graphing package) and VectorCalculus (just what it sounds like). These are loaded with the command

with(packagename):

For example,

with(VectorCalculus):

loads the VectorCalculus package. Do take note of capital letters; MAPLE is case-sensitive. MAPLE does not care about spaces, however, although you should not put spaces in the middle of single-word commands.

1. To draw a 2-dimensional graph, use the plot command; to draw a 3-dimensional graph, use the plot3d command. The plot command works as follows:

plot(f(x),x=a..b);

You must substitute your function for f(x) (like x2 in place of f(x)). The range x=a..b tells Maple over what range of values to evaluate the function. The view=[c..d,e..f] option can make the window larger (or smaller) than the evaluated range; see Maple's help for more details.

1. Multiplication requires an asterisk, *, located on the 8 key. Juxtaposition of symbols, like ab, is not sufficient; it must be a*b. Powers (exponents) use the carat key, ^, located on the 6.
2. To find the square root of a number, use the sqrt command, like

sqrt(x);

3. For natural logarithms, sines, cosines, etc., use standard notation: ln(x), sin(x), arctan(x), etc.

4. For the plot3d command, MAPLE assumes that the first argument is equal to z, so if you have z expressed explicitly as a function of x and y, just write in the function (but not z=). For example, to graph the function f(x,y) = x2 - y, use the command

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

If z is not expressed explicitly as a function of x and y, you will need to use implicitplot3d, in which the first argument is an equation. For example, to graph z2=x2+y2, use the command

implicitplot3d(z^2 = x^2 + y^2, x = -5..5, y = -5..5, z = -5..5);

Notice that with implicitplot, you must specify a range for x, y, and z, while for plot3d you need only specify the range for x and y.
5. In cylindrical coordinates, plot3d assumes that you are giving it r as a function of z and θ. In spherical coordinates, it assumes you are giving it ρ as a function of θ and φ.
Demonstration
MAPLE Worksheets
The twisted cubic (movie) Worksheet
A graph of z Worksheet
The path of a charged particle in a constant magnetic field oriented along the y-axis Worksheet
A line (given by parametric equations) being drawn Worksheet
Various graphs and animations illustrating the idea of traces. Worksheet
T, N, B, and the special planes associated with a space curve. Worksheet