Linear Systems of ODEs (Mathematica Tutorial)

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

VariationalBound (Variational Methods Package Symbol)

VariationalBound[f, u[x ], {x, x_min, x_max}, u_t, {a}, {b}, ...] finds values of the parameters a, b, ... of a trial function u_t that extremize the functional ...

Erfi (Built-in Mathematica Symbol)

Erfi[z] gives the imaginary error function erf(i z)/i.

HermiteH (Built-in Mathematica Symbol)

HermiteH[n, x] gives the Hermite polynomial H_n (x).

Backtrack (Combinatorica Package Symbol)

Backtrack[s, partialQ, solutionQ] performs a backtrack search of the state space s, expanding a partial solution so long as partialQ is True and returning the first complete ...

FrobeniusSolve (Built-in Mathematica Symbol)

FrobeniusSolve[{a_1, ..., a_n}, b] gives a list of all solutions of the Frobenius equation a_1 x_1 + ... + a_n x_n = b.FrobeniusSolve[{a_1, ..., a_n}, b, m] gives at most m ...

StreamPlot (Built-in Mathematica Symbol)

StreamPlot[{v_x, v_y}, {x, x_min, x_max}, {y, y_min, y_max}] generates a stream plot of the vector field {v_x, v_y} as a function of x and y. StreamPlot[{{v_x, v_y}, {w_x, ...

CellMargins (Built-in Mathematica Symbol)

CellMargins is an option for Cell that specifies the absolute margins in printer's points to leave around a cell.

ExtendedGCD (Built-in Mathematica Symbol)

ExtendedGCD[n_1, n_2, ...] gives the extended greatest common divisor of the integers n_i.

Specularity (Built-in Mathematica Symbol)

Specularity[s] is a graphics directive which specifies that surfaces of 3D graphics objects which follow are to be taken to have specularity s. Specularity[s, n] uses ...