CountRoots (Built-in Mathematica Symbol)

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.

DirectedInfinity (Built-in Mathematica Symbol)

DirectedInfinity[] represents an infinite numerical quantity whose direction in the complex plane is unknown. DirectedInfinity[z] represents an infinite numerical quantity ...

Export (Built-in Mathematica Symbol)

Export["file. ext", expr] exports data to a file, converting it to the format corresponding to the file extension ext. Export[file, expr, " format"] exports data in the ...

FourierCoefficient (Built-in Mathematica Symbol)

FourierCoefficient[expr, t, n] gives the n\[Null]^th coefficient in the Fourier series expansion of expr.FourierCoefficient[expr, {t_1, t_2, ...}, {n_1, n_2, ...}] gives a ...

ImageTransformation (Built-in Mathematica Symbol)

ImageTransformation[image, function] gives an image in which each pixel at position {x, y} corresponds to the position function[{x, y}] in image.ImageTransformation[image, ...

LegendreQ (Built-in Mathematica Symbol)

LegendreQ[n, z] gives the Legendre function of the second kind Q_n (z). LegendreQ[n, m, z] gives the associated Legendre function of the second kind Q_n^m(z).

ModularLambda (Built-in Mathematica Symbol)

ModularLambda[\[Tau]] gives the modular lambda elliptic function \[Lambda](\[Tau]).

StirlingS2 (Built-in Mathematica Symbol)

StirlingS2[n, m] gives the Stirling number of the second kind \[ScriptCapitalS]_n^(m).

TransferFunctionPoles (Built-in Mathematica Symbol)

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

Nonlinear Second-Order ODEs (Mathematica Tutorial)

The general form of a nonlinear second-order ODE is For simplicity, assume that the equation can be solved for the highest-order derivative y^ ′′(x) to give There are a few ...