Maple Command Quick-Reference
for MS125 Calculus I

The following is a concise list of functions which you may find useful for exploring Calculus I topics with Maple. This list is not intended to be comprehensive or complete, but it covers the major commands and topics with very brief descriptions and examples of some of the commands. For more complete documentation, including all of the options which can be used with a command, see Maple's built-in documentation for that command (under the ``Help'' menu, do a ``Topic Search'' for the particular command name).

Some Points of Syntax:

When entering algebraic expressions, you must use the ``*'' character to indicate multiplication -- for example, entering ``2x'' will give a syntax error; the correct form is ``2*x''. Maple is very picky about this.

To indicate exponents, use the ``^'' character -- for example, ``x^2'' represents .

Algebra:

simplify -- simplify an expression

> simplify((x^2+3*x+2)/(x+1));
x+2

expand -- expand a product of expressions

> expand((x+1)*(x-2)*(x+3));
x^3+2*x^2-5*x-6

factor -- factor an expression, such as a polynomial

> factor(x^3+2*x^2-5*x-6);
(x+1)*(x-2)*(x+3)

Limits and Continuity:

limit -- limit of an expression, as variable approaches constant

> limit(sin(x)/x, x=0);
1

This example computes .

discont -- find discontinuities in expression, with respect to given variable

> discont((x^2+3*x+2)/(x^2+3*x), x);
{-3,0}

To test using a purely numerical algorithm, use fdiscont.

iscont -- test continuity on an interval (returns ``true'' or ``false'')

> iscont(1/x, x=-1..1);
false

Derivatives:

D -- derivative of a function

> D(sin);
cos

diff -- derivative of an expression

> diff(sin(x),x);
cos(x)

Diff -- inert form of diff (doesn't actually compute the derivative, but useful for displaying derivatives in worksheets)

Maple's built-in documentation includes a page explaining ``D vs. diff'' -- in practice, you will probably be using diff rather than D. The diff command can also do derivatives at a particular -value:

> diff(sin(x),x=0);
1

See Maple's built-in documentation for diff to see more options.

implicitdiff -- compute derivative implicitly

> implicitdiff(x^2+y^2=1,y,x);
-x/y

Note: The above implicitdiff example computes -- to compute , enter:

> implicitdiff(x^2+y^2=1,x,y);

(Note the order of the variables.)

More Syntax:

You may sometimes want to apply a command to the result from the previous line in your worksheet -- for this, Maple provides the ``%'' character. For example, enter the following two lines into a worksheet and observe the results:

> diff((x^2+3*x+2)/x, x);
> simplify(%);

In case you ever need it, ``%%'' refers to the result from two lines back in your worksheet. There is no simple way to refer to the result from three lines back.

Integrals:

int -- integral
indefinite (antiderivative) form:

> int(cos(x),x);
sin(x)+C

definite integral form:

> int(cos(x),x=0..Pi/2);
1

Int -- inert form of int (doesn't actually compute the integral, but useful for displaying integrals in worksheets)

See Maple's built-in documentation for int to see more options.

Basic Graphing:

plot -- plot a graph of a function (probably the single most useful Maple command)

The plot command has lots of options -- see Maple's built-in documentation for details. You should be particularly careful about Maple's ability to automatically scale the coordinate axes. Graphs are not included here, but you should try the following commands to see the differences:

> plot(x^2, x=-10..10);
> plot(x^2, x=-10..10, y=-10..10);
> plot(x^2, x=-10..10,
scaling=constrained);

Loading Libraries:

with -- load a Maple library

> with(plots):

(Loads the ``plots'' library, see below.)

Still More Syntax:

You may note that the ``with'' command above ends with ``:'' rather than ``;'' -- Maple makes a distinction between a colon and semicolon at the end of a line. A semicolon (``;'') indicates that the command on that line is intended to generate output in the worksheet. A full colon (``:'') suppresses the output. The output from the ``with'' command is diagnostic messages indicating which functions are being loaded with the library. You have no need to see this output, so you might as well suppress it. Another command where you commonly see the full colon used is the ``reset'' command, which clears Maple's internal memory, allowing you to start computations over:

> reset:

Again, you have no need to see the output from this command, so you might as well suppress it.

Common Libraries:

Library: plots -- more sophisticating plotting routines than the plot command

implicitplot -- plots graph given implicitly, i.e. as an equation rather than as a function. For example, enter the following:

> with(plots):
> implicitplot(x^2+y^2=1,x=-4..4,
y=-4..4);

Library: student -- includes some useful calculus approximation techniques and visualizations

showtangent -- shows a graph and a tangent line at a specified -value

> with(student):
> showtangent(x^2,x=1);

The following three commands in the student library show graphs of approximations to a definite integral, using the Left Endpoint Rule, Midpoint Rule, and Right Endpoint Rule, respectively:
leftbox
middlebox
rightbox
See the Maple buil-in documentation for complete syntax -- it is similar to int above, with options similar to plot.

The following five commands in the student library compute approximations to a definite integral integral:
leftsum
middlesum
rightsum
simpson
trapezoid
Again, syntax is similar to int above, but since nothing is graphed with these commands, there are no plot options.

Library: student[Calculus1] -- a package with some interesting graphical visualizations for topics in Calculus I

> with(student[Calculus1]):

Here is a list of some of the commands in the student[Calculus1] library:
DerivativePlot
Tangent
RollesTheorem
MeanValueTheorem
Asymptotes
CricicalPoints
ExtremePoints
InflectionPoints
FunctionChart
NewtonQuotient
Antiderivative
RiemannSum
ApproximateInt
FunctionAverage
Again, see Maple's built-in documentation for details.

Again, please keep in mind that this list of commands is not intended to be in any way complete, comprehensive, or detailed. You should think of this list as a way to help you find the right command in Maple's built-in documentation. For the details of a command's options and syntax, refer to Maple's built-in documentation.