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 ...

Plots of data based on measurements often have vertical lines or intervals centered at the points to indicate the associated error estimates. Mathematica lets you add such ...

ListLogPlot[{y_1, y_2, ...}] makes a log plot of the y_i, assumed to correspond to x coordinates 1, 2, ....ListLogPlot[{{x_1, y_1}, {x_2, y_2}, ...}] makes a log plot of the ...

EventHandler[expr, {"event_1" :> action_1, "event_2" :> action_2, ...}] displays as expr, evaluating action_i whenever "event_i" occurs in connection with expr.

Filling is an option for ListPlot, Plot, Plot3D, and related functions that specifies what filling to add under points, curves, and surfaces.

Normal[expr] converts expr to a normal expression, from a variety of special forms.

s_1 ~~ s_2 ~~ ... or StringExpression[s_1, s_2, ...] represents a sequence of strings and symbolic string objects s_i.

Tuples[list, n] generates a list of all possible n-tuples of elements from list. Tuples[{list_1, list_2, ...}] generates a list of all possible tuples whose i\[Null] ...

Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...

ElementAbsorptionMap[element] generates a plot of the absorption map of the element element.ElementAbsorptionMap[element, ionstage] generates a plot for the ionization level ...