Nonlinear Systems of ODEs (Mathematica Tutorial)

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

LQGRegulator (Built-in Mathematica Symbol)

LQGRegulator[{ss, sensors, finputs}, {w, v, h}, {q, r, p}] constructs the optimal feedback regulator for the StateSpaceModel ss using noisy measurements sensors and feedback ...

PowerMod (Built-in Mathematica Symbol)

PowerMod[a, b, m] gives a^b mod m. PowerMod[a, -1, m] finds the modular inverse of a modulo m.PowerMod[a, 1/r, m] finds a modular r\[Null]^th root of a.

Reals (Built-in Mathematica Symbol)

Reals represents the domain of real numbers, as in x \[Element] Reals.

TrigFactor (Built-in Mathematica Symbol)

TrigFactor[expr] factors trigonometric functions in expr.

PoincareSection (Equation Trekker Package Symbol)

PoincareSection is a setting for the option TrekGenerator that specifies that the Poincaré section for differential equations is used to generate treks.

Multivariate Statistics Package (Multivariate Statistics Package Tutorial)

This package contains descriptive statistics for multivariate data and distributions derived from the multivariate normal distribution. Distributions are represented in the ...

RootApproximant (Built-in Mathematica Symbol)

RootApproximant[x] converts the number x to one of the "simplest" algebraic numbers that approximates it well.RootApproximant[x, n] finds an algebraic number of degree at ...

FourierCosSeries (Built-in Mathematica Symbol)

FourierCosSeries[expr, t, n] gives the n\[Null]^th-order Fourier cosine series expansion of expr in t.FourierCosSeries[expr, {t_1, t_2, ...}, {n_1, n_2, ...}] gives the ...

InverseSurvivalFunction (Built-in Mathematica Symbol)

InverseSurvivalFunction[dist, q] gives the inverse of the survival function for the symbolic distribution dist as a function of the variable q.