Maple is a Computer Algebra System (CAS), that is, a computer program that can do algebra. In this assignment we explore some of its abilities.
Basic Commands and Basic Syntax
Generalities
Lines should end with a “;”
Products must be explicit: 2*x not 2x. Maple knows π as Pi, √
as sqrt( ), ex as exp(x), ln(x) as • Extraneous lines can be deleted by pressing Ctrl and Delete simultaneously.
log(x), and logb(x) as logb. Angles are in radians.
Assign a name to an output with name := …. It is good practice to name output so you do not have
to recopy it.
A Maple set is a comma-separated list enclosed in braces. Braces identify the contents as forming a set. Sets have no prescribed order and no repeated elements.
A Maple list is a comma-separated list enclosed in square brackets. Lists have a prescribed order, and repeats are allowed.
Ranges are of the form left endpoint..right endpoint .
A string of characters in an execution group ([>) rather than a Text group is enclosed in double quotes.
Useful Commands
solve(equation, variable ) solves the given equation for the given variable. If instead of an equation you have an expression, Maple sets the expression to 0 and then solves. If you have a set or list of equations (enclosed in braces or square brackets respectively) in several variables, and you have a set or list of variables, Maple will try to solve the equations simultaneously for all variables.
eval(expression, variable=value or list of variable=values ) substitutes in the given values for the variables.
evalf(number ) returns a decimal value for the exact number. Maple tries to calculate answers exactly, so it keeps all nasty roots.
fsolve(equation in one variable, variable or variable=range) finds a numeric solution to the equation. If the range is specified, it looks for a solution in the given interval. It is always good practice to specify a range
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simplify(expression ) simplifies the expression. The simplify command does not always do what you want, so Maple has more explicit simplification commands, such as expand, collect, rationalize, combine, and factor.
limit(expression, variable=number, optional direction) finds lim f(x) where f(x) is the ex- x→a
pression and x the variable. The direction need not be present, but if it is, is one of left or right, and specifies whether a left-hand or right-hand limit is taken.
diff(expression, variable) differentiates the expression with respect to the given variable. If the variable is followed by $number, for example, in diff(x*sin(x), x$3, diff finds the numberth derivative with respect to the given variable.
plot(expression or list of expressions, variable=range, optional y range ) plots y =expression or the list of expressions over the given range of the independent variable. If the y range is given, it displays only y coordinates in that range. There are many optional arguments such as “discont=true”
or “linestyle=line style or list of line styles ” or “colour=colour or list of colours ” which further affect the appearance of the graph.
Sample Solution