Linear Higher-Order Equations with ... (Mathematica Tutorial)

A linear ODE with constant coefficients can be easily solved once the roots of the auxiliary equation (or characteristic equation) are known. Some examples of this type ...

Linear Second-Order Equations with ... (Mathematica Tutorial)

The simplest type of linear second-order ODE is one with constant coefficients. This linear second-order ODE has constant coefficients. Notice that the general solution is a ...

Continuous Distributions (Mathematica Tutorial)

The functions described here are among the most commonly used continuous univariate statistical distributions. You can compute their densities, means, variances, and other ...

Plotting Search Data (Mathematica Tutorial)

The utility functions FindMinimumPlot and FindRootPlot show search data for FindMinimum and FindRoot for one- and two-dimensional functions. They work with essentially the ...

Variables and Starting Conditions (Mathematica Tutorial)

All the functions FindMinimum, FindMaximum, and FindRoot take variable specifications of the same form. The function FindFit uses the same form for its parameter ...

AiryAi (Built-in Mathematica Symbol)

AiryAi[z] gives the Airy function Ai(z).

AiryBi (Built-in Mathematica Symbol)

AiryBi[z] gives the Airy function Bi(z).

BetaRegularized (Built-in Mathematica Symbol)

BetaRegularized[z, a, b] gives the regularized incomplete beta function I_z (a, b).

EllipticK (Built-in Mathematica Symbol)

EllipticK[m] gives the complete elliptic integral of the first kind K(m).

EllipticTheta (Built-in Mathematica Symbol)

EllipticTheta[a, u, q] gives the theta function \[CurlyTheta]_a (u, q) (a = 1, ..., 4).