The Essential Maple

Scott Esterholm and Mark Pond

Critical Functions

restart; - Command to reset all variables. Should be used at top of every program.

?command – Calls up Maple help on a command.

; - Executes command line and shows result.

: - Executes command line and hides result.

:= - Variable assignment operator. (NOT =)

funct := var -> expr(var); - Creates a function with respect to a variable

simplify(expr, assume=positive); - Simplifies the format of an expression as stored by

Maple. This format of simplify will take care of extraneous radicals.

convert(expr, form); - Converts an expression to a certain format. Examples of forms

include exp, trig, D, diff or even units when done in the following way:

convert(num, units, oldUnits, newUnits); For a complete list, use ?convert.

evalf(expr); - Evaluates with floating point numbers. (gets rid of fractions / Pi)

solve(expr, var); - Solves an expression for a specified variable.

solve({expr1, …, exprN},{var1, …, varN}); - Solves n equations for n unknowns.

diff(expr, var); - Takes the first derivative of the expression with respect to the variable.

diff(expr, var1, …., varN); - Takes derivative with respect to all N variables.

D(funct); - Takes derivative of function.

D[M](funct)(var1, …, varN); - Takes derivative of multi-variable function with respect to

Mth variable.

int(expr, var); - Takes indefinite integral with respect to the variable.

int(expr, var = A…B); - Takes definite integral with respect to the variable from A to B.

dsolve(deq, funct(var)); - Solves differential equation for given function.

dsolve({deq, BC1, …, BCN}, funct(var)); - Solves differential equation for given

function and boundary conditions.

assign(soln); funct := unapply(funct(var), var); - Takes a solution from a solver and

assigns it as a function.

[v1, …, vN]; - Makes a vector with N entries.

[[a11, …, a1N], …, [aM1, …, aMN]]; - Makes a M x N array

map(funct, expr); - A linear mapping of a function onto an expression (which can be a

vector or array).

dchange(transforms, expr, [NewVar1, …, NewVarN]); - Performs a change of

variables on an expression. First must use the following command: with(PDEtools);.

The variable transforms should be defined as the following:

transforms := {var1 = expr1, …, varN = exprN}; where the expressions are in terms

of the new variables.

LeastSquares(xdata, ydata, xvar, curve = expr(x)); - Performs a least squares

regression for a set of data. First must use the following command: with(CurveFitting);.

For a linear regression, expr(x) should be ‘A*x+B’.

LeastSquares(xydata, xvar, curve = expr(x)); - Same function as above, except

xydata is an array of the form [[x1,y1], …, [xN,yN]].

Plot Functions

plot(funct(var), var = A…B); - Plots a function over a given interval.

plot(xydata); - Plots a set of points. xydata is an array of the form [[x1,y1], …, [xN,yN]].

If the data is in two separate vectors of length N, xdata and ydata, then they can

be merged into a single vector, xydata, with the following command:

xydata := [[xdata[j], ydata[j]]$j=1…N];

plot({funct1(var), …, functN(var), xydata1, …, xydataN}, var = A…B); - Plots multiple

functions and data sets over a given interval.

Plot Formatting Example

plot({xydata1, xydata2, xydata3}, labels = [“x”,”y”], title = “Example Plot”,

style = [line, point, point], color = [red, blue, black]);

The labels command labels the x and y axes. The title command gives the plot a title.

The style command will differentiate between data expressed as points and lines. The color

command changes the color of a set of data. There is also a legend command, which can only

be used for functions.

Helpful Hints

Unit Conversion – Make statements of the following form:

DesiredUnit := x*CurrentUnit;

where x is equal to DesiredUnit divided by CurrentUnit

# - Comment on a command line

CTRL + K - Insert Execution Group ABOVE Cursor

CTRL + J - Insert Execution Group BELOW Cursor

CTRL + SHIFT + K - Insert Comment ABOVE Cursor

CTRL + SHIFT + J - Insert Comment BELOW Cursor

SHIFT + ENTER - Moves cursor to new line in execution group (for ease of reading)

!!! (Button at Top) - Executes entire program

Red Octagon (i.e. Stop Sign Button at top toolbar) - Halts program execution

Note: Most graphical and matrix applications should be done in Matlab.

(Updated April 2005)

Link to Downloadable Microsoft Word Document

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Project by: Scott Esterholm and Mark Pond

CENG 402

2005