Sech[z] gives the hyperbolic secant of z.

Sinh[z] gives the hyperbolic sine of z.

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, ...

Tanh[z] gives the hyperbolic tangent of z.

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

NIntegrate[f, {x, x_min, x_max}] gives a numerical approximation to the integral \[Integral]_x_min^x_max\ f\ d \ x. NIntegrate[f, {x, x_min, x_max}, {y, y_min, y_max}, ...] ...

Mathematica 6.0 fundamentally redefined Mathematica and introduced a major new paradigm for computation. Building on Mathematica's time-tested core symbolic architecture, ...

ListPlot[{y_1, y_2, ...}] plots points corresponding to a list of values, assumed to correspond to x coordinates 1, 2, .... ListPlot[{{x_1, y_1}, {x_2, y_2}, ...}] plots a ...

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

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 ...