List of Common Commands

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Appendix B List of Common Commands

Keyboard Shortcuts
Ctrl+J, Ctrl+K	New execution group (after or before current line) 🔗
Ctrl+Shift+J, Ctrl+Shift+K	New paragraph (after or before current line) 🔗
Ctrl+T	Convert line to Paragraph 🔗
Ctrl+M	Convert line to Maple input 🔗
Ctrl+.	Indent section 🔗
Ctrl+,	Unindent section 🔗
Ctrl+Delete	Delete section 🔗
F4	Merge consecutive execution groups 🔗
F5	Toggle between Text, Nonexecutable Math, and Math types 🔗

Common Expressions
exp(x)	The natural exponential function 🔗
sqrt(x)	The square root function 🔗
surd(x,n)	The primitive \(n\)th root, \(\sqrt[n]{x}\) 🔗
abs()	The absolute value function 🔗

Manipulating Expressions
name := expression	Assignment operator 🔗
subs(x=a, expression)	Evaluate an expression at \(x = a\) 🔗
evalf(expression)	Evaluate the given expression as a decimal 🔗
factor(expression)	Factor the given expression 🔗
simplify(expression)	Simplify the given expression 🔗
expand(expression)	Expand the given expression 🔗
collect(expression,var)	Collect terms of the expression by the specified variable 🔗

Solving Equations
solve(equation,var)	Solves the given equation for the specified variable 🔗
fsolve(equation,var)	Solves the given equation for the specified variable (as a decimal) 🔗
fsolve(equation,var=a..b)	Solves the given equation for the specified variable (as a decimal) on the interval \([a,b]\) 🔗
solve( {eqn1,eqn2},{var1,var2})	Solves a system of equations for all specified variables 🔗
fsolve({eqn1,eqn2},{var1,var2})	Solves a system of equations for all specified variables (as a decimal) 🔗

Defining Functions
name(var) := expression	Assigns a function of the specified variable 🔗
name := unapply(expression,var)	Convert an expression to a function of the specified variable 🔗
name(var) := piecewise(condition,expr, ..., condition,expr) 🔗	Create a piecewise function of the specified variable where each condition is an interval 🔗
	🔗

Plotting Functions
plot(f(x),x=a..b)	Plot the given function, \(f(x)\text{,}\) over the interval \([a,b]\) 🔗
plot([f(x),g(x)],x=a..b)	Plot two functions, \(f(x)\) and \(g(x)\text{,}\) over the interval \([a,b]\) 🔗

Additional Plot Parameters (Include these after necessary parameters)
y=c..d	Only plot the range \(c \leq y \leq d\) 🔗
discont=true	Includes discontinuities in a plot 🔗
colour=blue	Specify the colour for a graph (black, blue, red, etc.) 🔗
linestyle=dotted	Specify the style of the line (dash, dot, etc.) 🔗

Limits
limit(expression,var=a)	Find the limit of the expression as var approaches \(a\) 🔗
limit(expression,var=a,right)	Find the limit of the expression as var approaches \(a\) from the right 🔗
limit(expression,var=a,left)	Find the limit of the expression as var approaches \(a\) from the left 🔗
limit(expression,var=infinity)	Find the limit of the expression as var approaches infinity 🔗

Derivatives
diff(expression,var)	The derivative of the given expression with respect to variable 🔗
diff(expression,var,var)	The second derivative of the given expression with respect to variable 🔗
diff(expression,var$2)	The second derivative of the given expression with respect to variable 🔗
f’(var)	The derivative of the function \(f\) with respect to variable 🔗
f^(n)(var)	The \(n\)th derivative of the function \(f\) with respect to variable 🔗

Implicit Functions (requires "plots" package for plotting)
implicitplot(equation,x=a..b,y=c..d)	Plot the implicit function over the specified region 🔗
implicitdiff(equation,y,x)	The derivative of the implicit function, given as \(dy/dx\) 🔗

Riemann Sums and Numerical Integration (requires "Student[Calculus1]" package)
ApproximateInt(f(x),x=a..b)	Approximate the definite integral of \(f(x)\) from \(x=a\) to \(x=b\) 🔗

Additional ApproximateInt Parameters (Include these after necessary parameters)
method=left	Choose left rectangles for approximation 🔗
method=right	Choose right rectangles for approximation 🔗
method=lower	Choose lower bound rectangles for approximation 🔗
method=upper	Choose upper bound rectangles for approximation 🔗
method=midpoint	Choose midpoint rectangles for approximation 🔗
method=trapezoid	Choose trapezoid rule approximation 🔗
method=simpson	Choose Simpson’s rule approximation 🔗
output=sum	Output summation notation for given approximation method 🔗
output=value	Output exact value of approximation 🔗
output=plot	Output graph of integrand function and approximation 🔗
output=animation	Output animation of approximation as \(n\) increases 🔗
partition=n	Use \(n\) equally spaced subintervals for approximation 🔗

Sequences and Series
expression $ var=a..b	Display the sequence of the expression from var = \(a\) up to var = \(b\) 🔗
seq(expression,var=a..b)	Display the sequence of the expression from var = \(a\) up to var = \(b\) 🔗
Sum(expression,var=a..b)	Display the sum for the expression from var = \(a\) up to var = \(b\) 🔗
sum(expression,var=a..b)	Give the value of the sum of the expression from var = \(a\) up to var = \(b\) 🔗
taylor(f(x),x=a,n)	Give the Taylor series expansion of \(f(x)\) about \(x=a\text{,}\) including terms up to power \(n-1\) 🔗

Integrals
Int(f(x),x)	The indefinite integral, display "inert" form 🔗
int(f(x),x)	The indefinite integral, evaluated 🔗
Int(f(x),x=a..b)	The definite integral over the specified interval, display "inert" form 🔗
int(f(x),x=a..b)	The definite integral over the specified interval, evaluated 🔗

Differential Equations
dsolve(DE, y(x))	Solves the given differential equation for \(y(x)\) 🔗
dsolve([DE, ICs], y(x))	Solves the given differential equation with initial conditions for \(y(x)\) 🔗

Direction Fields (Requires DEtools package)
DEplot(DE,y(x),x=a..b,y=a..b)	Plot the direction field for the differential equation \(dy/dx\) 🔗
DEplot(DE,y(x),x=a..b,y=a..b,[ICs])	Plot the direction field for the differential equation \(dy/dx\) with initial conditions 🔗

Additional DEplot Parameters (Include these after necessary parameters)
arrows=line	Use lines for the direction field, rather than arrows 🔗
colour=black	Change arrow colour 🔗
linecolour=blue	Change solution curve colour 🔗