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 ...

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

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Some operators used in basic arithmetic and algebra. Note that the  for ∖[Cross] is distinguished by being drawn slightly smaller than the × for ∖[Times]. Interpretation of ...

Mathematica provides a large number of options for cells. All of these options can be accessed through the Option Inspector menu item in the front end. They can be set either ...

Mathematica provides a general mechanism for specifying constraints on patterns. All you need to do is to put /;condition at the end of a pattern to signify that it applies ...

.NET/Link lets you write sophisticated user interfaces by calling .NET types directly from Mathematica. Doing so allows you to evaluate code as you add it, either one or ...

ArrayPlot[array] generates a plot in which the values in an array are shown in a discrete array of squares.

Series[f, {x, x_0, n}] generates a power series expansion for f about the point x = x_0 to order (x - x_0) n. Series[f, {x, x_0, n_x}, {y, y_0, n_y}, ...] successively finds ...

SmoothHistogram3D[{{x_1, y_1}, {x_2, y_2}, ...}] plots a 3D smooth kernel histogram of the values {x_i, y_i}.SmoothHistogram3D[{{x_1, y_1}, {x_2, y_2}, ...}, espec] plots a ...