TransferFunctionPoles[tf] gives a matrix of roots of the denominators in the TransferFunctionModel object tf.

lhs != rhs or lhs != rhs returns False if lhs and rhs are identical.

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

WeierstrassPPrime[u, {g_2, g_3}] gives the derivative of the Weierstrass elliptic function \[WeierstrassP](u; g_2, g_3).

The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...

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.

[AB04] Abell, M. L. and J. P. Braselton. Differential Equations with Mathematica. (3rd ed.) Elsevier Academic Press, 2004. [A89] Abramov, S. A. "Rational Solutions of Linear ...

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

When Mathematica reads the text x^y, it interprets it as x raised to the power y. In a notebook, you can also give the two-dimensional input x^y directly. Mathematica again ...

Mathematica provides built-in support for both programmatic and interactive image processing, fully integrated with Mathematica's powerful mathematical and algorithmic ...