Special Functions (Mathematica Tutorial)

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

SymplecticPartitionedRungeKutta Method ... (Mathematica Tutorial)

When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

LyapunovSolve (Built-in Mathematica Symbol)

LyapunovSolve[a, c] finds a solution x of the matrix Lyapunov equation a.x + x.a\[ConjugateTranspose] == c.LyapunovSolve[a, b, c] solves a.x + x.b == c.LyapunovSolve[{a, d}, ...

HypergeometricU (Built-in Mathematica Symbol)

HypergeometricU[a, b, z] is the confluent hypergeometric function U(a, b, z).

Select (Built-in Mathematica Symbol)

Select[list, crit] picks out all elements e_i of list for which crit[e_i] is True. Select[list, crit, n] picks out the first n elements for which crit[e_i] is True.

Delay Differential Equations (Mathematica Tutorial)

A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: ...

DiscreteLQRegulatorGains (Built-in Mathematica Symbol)

DiscreteLQRegulatorGains[ss, {q, r}, \[Tau]] gives the optimal discrete-time state feedback gain matrix with sampling period \[Tau] for the continuous-time StateSpaceModel ...

EllipticThetaPrime (Built-in Mathematica Symbol)

EllipticThetaPrime[a, u, q] gives the derivative with respect to u of the theta function \[CurlyTheta]_a (u, q) (a = 1, ..., 4).

FresnelC (Built-in Mathematica Symbol)

FresnelC[z] gives the Fresnel integral C(z).

FresnelS (Built-in Mathematica Symbol)

FresnelS[z] gives the Fresnel integral S(z).