Density and contour plots. This gives a density plot of sin(x) sin(y). Lighter regions show higher values of the function. Some options for DensityPlot.

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...

ArcTan[z] gives the arc tangent tan -1 (z) of the complex number z. ArcTan[x, y] gives the arc tangent of y/x, taking into account which quadrant the point (x, y) is in.

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

The IDA package is part of the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) developed at the Center for Applied Scientific Computing of Lawrence ...

Element[x, dom] or x \[Element] dom asserts that x is an element of the domain dom. Element[{x_1, x_2, ...}, dom] asserts that all the x_i are elements of dom. Element[patt, ...

Catalan is Catalan's constant, with numerical value \[TildeEqual] 0.915966.

A "How to" describes how to carry out particular tasks with Mathematica, giving step-by-step instructions for common cases.

A foundational idea in Mathematica is that all expressions—whatever they may represent—ultimately have a uniform tree-like structure.

Since many functions in Mathematica give solutions in the form of rules, you need to be able to use these rules to explore and interpret your results. Although many of the ...