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Constructing algebraic objects

How do I...

enter a piecewise expression or function

 • Example 1.1: Use the piecewise template from the Expression palette
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enter an algebraic equation

 • See Example 1.2.

create a sequence

 • Context Panel: Sequence
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construct a loop

 • See Example 1.3.

write the exponential function ${ⅇ}^{x}$

 • Example 1.4: Use the exponential template from the Expression palette or use Command Completion in Math mode

enter ${\mathrm{log}}_{a}\left(x\right)$

 • In Math mode, the expression can be entered normally with the $a$ entered as a subscript.  To enter the subscript level, hold down [Ctrl] and press underscore [_]; after typing the subscript, press the right arrow key to leave the subscript.  Finish the expression by entering $\left(x\right)$
 • Example 1.5: Use the log template from the Expression palette
 • In Maple Input mode, log[a](x) can be used to represent ${\mathrm{log}}_{a}x$

convert an expression to a function

 • Context Panel: See Example 1.6
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write a procedure

Algebraic manipulations

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obtain the equation of a line

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obtain the coordinates of the midpoint of a line segment

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obtain the slope of a line segment

 • Task: Line Segment - Slope

compute the distance between two points

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complete the square

 • Context Panel: Complete Square

square both sides of an equation

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 • Context Panel: Manipulate Equation

substitute into an expression

 • Context Panel: Evaluate at a Point
 • Context Panel: Constructions → Evaluate At → [variable name] (yields unevaluated evaluation)
 • Use the template $\genfrac{}{}{0}{}{{f}\left({x}\right)}{\phantom{x=a}}|\genfrac{}{}{0}{}{\phantom{\mathrm{f\left(x\right)}}}{{x}={a}}$from the Expression palette; replace with the expression on which to perform the substitution, and overwrite ${x}={a}$ with either the variable name equated to a value or a list of such equations
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 • Use the command eval to substitute a variable or value into an expression

substitute into an equation

 • Use any of the devices for substitution into an expression, except that the Context Panel for an equation does not provide the Constructions option

obtain the solution to RootOf

 • Context Panel: All Values
 • Context Panel: Conversions → To Radical
 • Use the allvalues command.

force an equation to be an identity

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 • Use the command solve(identity(eqn, x), vars); the expression (or equation) eqn is considered an identity in terms of the variable x, and solve attempts to find a solution in terms of vars that satisfies eqn for any value of x.

determine the inverse of a function

 • Function Inverse Tutor: interpolate data

 • Context Panel: Curve Fitting → any of B-Spline, Interactive Curve Fitting, Least Squares, Polynomial Interpolation, Rational, Spline, Thiele
 • Curve Fitting Assistant: This assistant also allows you to import data into Maple from an external file to produce plots of various interpolating functions (Example 2.1)
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obtain a partial fraction decomposition of a rational function

 • Context Panel: Conversions → Partial Fractions → [variable name]
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 • The command convert(f, parfrac, x) converts a function, f with main variable, x into partial fractions.

obtain real values of ${x}^{1/3}$

 • Use the surd command.

Algebraic solvers

How do I...

solve algebraic equation(s)

 • Context Panel: Solve → any of Isolate Expression for, Numerically Solve, Numerically Solve from point, Obtain Solutions for, Solve, Solve (explicit), Solve (general solution), Solve for Variable
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solve an inequality

 • Context Panel: Solve

eliminate parameter in parametric equations

 • Context Panel: Solve → Eliminate a Variable → [parameter name]

eliminate selected variables in a set or list of equations

 • Context Panel: Solve → Eliminate Variables
 • Use the eliminate command

Polynomial arithmetic

How do I...

multiply out the factored form of a polynomial

 • Context Panel: Expand

factor a polynomial

 • Context Panel: Factor

find the zeros of a polynomial

 • Context Panel: Solve

obtain the quotient and remainder when dividing polynomials

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Plotting

How do I...

graph a curve or a surface

 • For an expression, Context Panel: Plots → Plot Builder
 • For a function, Context Panel: Plots → 2-D Plot or 3-D Plot
 • See the comprehensive Plotting Guide

create an animation

 • Context Panel: Plots → Plot Builder → Select Plot Type and Functions → Animation
 • Use the animate command in the plots package

animate the drawing of a plane curve

 • Use the animatecurve command in the plots package

trace coordinates along a plane curve

 • Context Panel (for graph): Probe Info → Nearest point on line

create a graph with one or more parameters controlled by sliders

 • Context Panel: Plots → Plot Builder → Select Plot Type and Functions → Interactive Plot with (n) parameter(s)

graph a rational function and its asymptotes

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 • Rational Function Tutor: graph linear inequalities

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 • Linear Inequalities tutor • Use the inequal command in the plots package

graph conic sections

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 • Conic Sections tutor graph the intersection of two surfaces

Use the intersectplot command from the plots package

Differential calculus in one variable

How do I...

construct a limit

 • Context Panel: Constructions → Limit → [variable name] and input the value
 • Limit Methods tutor: See Example 6.1

evaluate a limit

 • Context Panel: Limit
 • Limit Methods tutor • Task: Limit - Formal Rules

display an annotated stepwise evaluation of a limit

 • Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1) Calculus palette: enter and complete $\underset{{x}\to {a}}{lim}{f}$, the limit template Context Panel: 2-D Math → Convert To → Inert Form Context Panel: Solve → Show Solution Steps

differentiate

 • Context Panel: Differentiate → [variable name]
 • Differentiation Methods tutor or See Example 6.2
 • Use the template $\frac{ⅆ}{ⅆ\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}$ from the Calculus palette: See Example 6.3

exhibit annotated stepwise evaluation of a derivative

Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1)
Calculus palette: enter and complete $\frac{ⅆ}{ⅆ\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}$, the differentiation template
Context Panel: 2-D Math → Convert To → Inert Form
Context Panel: Solve → Show Solution Steps

differentiate implicitly

 • Context Panel: Differentiate → Implicitly
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 • Use the implicitdiff command

graph a function and its derivative(s)

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 • Derivatives tutor or See Example 6.4

obtain equations for tangent and normal lines along a curve

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analyze a plane curve