Maple Commands for Math

Maple Commands for Mathematics

• > restart clears all variables and unloads all packages.
• > eval evaluates an expression.
• > evalf(Pi, 5) evaluates π to 5 digits.
• > subs(x = 2 * x * y, x^2) substitutes 𝑥 = 2 ∗ 𝑥 ∗ 𝑦 into 𝑥^2, resulting in (2 ∗ 𝑥 ∗ 𝑦)^2 = 4𝑥^2𝑦^2.
• > diff(5 * x * y, x) differentiates with respect to 𝑥.
• > diff(5 * x * y, x$2) differentiates with respect to 𝑥 twice.
• > simplify(x * y + 2 * x * y - 3 * x) simplifies the expression.
• > expand((x + 1)(x + 2)) expands a factored expression.
• > factor(x^2 + 2x + 1) factors an expression.
• > exp(Pi * I) represents the exponential function e^(πi).
• > solve(5 * x + x * y^2 = 3, x) solves the equation for 𝑥.
• > solve({eq1, eq2, eq3}, [x, y, z]) solves a system of 3 equations for 𝑥, 𝑦, and 𝑧 variables.
• > plot(f(x), x = a..b) plots a function 𝑓 for the domain 𝑥 = 𝑎 to 𝑥 = 𝑏.
• > plot({f(x), g(x), ..., h(x)}, x = a..b) plots several functions for the domain 𝑥 = 𝑎 to 𝑥 = 𝑏 on the same graph.
• > plot([f(t), g(t), t = a..b]) plots a parametric curve.
• > plot([f(t), g(t), t = a..b], [h(t), j(t), t = c..d]) plots several parametric curves.
• > Matrix(2) generates a null matrix of order 2 × 2.
• > Matrix(2,3) generates a null matrix of order 2 × 3.
• > Matrix(3, shape = identity) generates an identity matrix of order 3 × 3.
• > Matrix(1..3, 1..3, 5) creates a matrix of order 3 × 3 with all entries equal to 5.
• > Matrix([1,2,3], [4,5,6]) arranges the matrix as [[1, 2, 3], [4, 5, 6]].
• < 1|2,3|4,5,6|7,8,9 > arranges the matrix as [[1, 4, 7], [2, 5, 8], [3, 6, 9]].
• > Vector([0,0,0]) OR > Vector(3, shape = 'zero') creates a column vector as [0, 0, 0].
• > Vector[row](3, 'fill' = 1) creates a row vector as [1, 1, 1].
• > with(plots, implicitplot) is a command for implicit functions.
• > mplicitplot(f, x = a..b, y = c..d, options) is used for plotting implicit functions.
• > limit(f, x = a) computes the limit of 𝑓 as 𝑥 approaches 𝑎.
• > limit(f, x = a, left) computes the left-hand limit of 𝑓 as 𝑥 approaches 𝑎.
• > iscont(expression, x = a..b, 'closed') checks whether a function is continuous within the given closed interval.
• > g := piecewise(x < 3, x^2 - 6, 3 <= x, 2*x - 1) creates a piecewise function.
• > diff(f(x), x$n) computes the nth derivative of a function 𝑓.
• > taylor(f(x), x = a, n) generates a Taylor polynomial for a function about a point 𝑎.
• > maximize(f(x), x = a..b) finds the maximum value of a function from 𝑥 = 𝑎 to 𝑥 = 𝑏.
• > minimize(f(x), x = a..b) finds the minimum value of a function from 𝑥 = 𝑎 to 𝑥 = 𝑏.
• > int(f(x), x = a..b) computes a definite integral of the function.
• > diff(f(x, y), x) partially differentiates a function with respect to 𝑥.
• > diff(f(x, y), x, y) partially differentiates a function first with respect to 𝑥, then with respect to 𝑦.
• > fsolve(polynomial) computes an approximate root(s) of the given polynomial.
• > fsolve(f(x, y), g(x, y), x, y) computes the approximate point(s) of intersection of two polynomials 𝑓 and 𝑔.
• > fsolve(f(x, y), g(x, y), x = a..b, y = c..d) computes an approximate point of intersection(s) of two polynomials 𝑓 and 𝑔 within specified intervals.
• > with(students[Calculus1]) loads the Calculus1 package for student calculus tools.
• > ApproximateInt(f(x), x = a..b, method = trapezoid, output = plot, partition = n) draws a plot of a function showing the area under the curve using the trapezoidal rule with 𝑛 subintervals.
• > ApproximateInt(f(x), x = a..b, method = simpson, output = plot, partition = n) draws a plot of a function showing the area under the curve using Simpson's rule with 𝑛 subintervals.