Roots[lhs == rhs, var] yields a disjunction of equations which represent the roots of a polynomial equation.

The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathematica function NDSolve, on the other hand, is a general numerical differential ...

BernsteinBasis[d, n, x] represents the n\[Null]^th Bernstein basis function of degree d at x.

Many large-scale applications of linear algebra involve matrices that have many elements, but comparatively few that are nonzero. You can represent such sparse matrices ...

FindRoot[f, {x, x_0}] searches for a numerical root of f, starting from the point x = x_0.FindRoot[lhs == rhs, {x, x_0}] searches for a numerical solution to the equation lhs ...

With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. ...

Basic plotting functions. This plots a graph of sin(x) as a function of x from 0 to 2π. You can plot functions that have singularities. Mathematica will try to choose ...

MonomialList[poly] gives the list of all monomials in the polynomial poly.MonomialList[poly, {x_1, x_2, ...}] gives the list of monomials with respect to the variables x_i in ...

ContourPlot[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a contour plot of f as a function of x and y. ContourPlot[f == g, {x, x_min, x_max}, {y, y_min, y_max}] plots ...

TransferFunctionExpand[tf] expands polynomial terms in the numerators and denominators of the TransferFunctionModel object tf.