RootIntervals[{poly_1, poly_2, ...}] gives a list of isolating intervals for the real roots of any of the poly_i, together with a list of which polynomials actually have each ...

SingularValuePlot[m] gives the singular value plot of a matrix m of rational functions in one complex variable.SingularValuePlot[sys] gives the singular value plot of a ...

StandardDeviation[list] gives the sample standard deviation of the elements in list. StandardDeviation[dist] gives the standard deviation of the symbolic distribution dist.

StringReplace["string", s -> sp] or StringReplace["string", {s_1 -> sp_1, s_2 -> sp_2, ...}] replaces the string expressions s_i by sp_i whenever they appear as substrings of ...

Variance[list] gives the sample variance of the elements in list. Variance[dist] gives the variance of the symbolic distribution dist.

VectorAngle[u, v] gives the angle between the vectors u and v.

Finding singular values and norms of matrices. The singular values of a matrix m are the square roots of the eigenvalues of m.m^*, where * denotes Hermitian transpose. The ...

The general principle that Mathematica follows in evaluating expressions is to go on applying transformation rules until the expressions no longer change. This means, for ...

Density and contour plots. This gives a density plot of sin(x) sin(y). Lighter regions show higher values of the function. Some options for DensityPlot.

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...