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 ...

UnitStep[x] represents the unit step function, equal to 0 for x < 0 and 1 for x >= 0. UnitStep[x_1, x_2, ...] represents the multidimensional unit step function which is 1 ...

Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number ...

FindList["file", " text"] gives a list of lines in the file that contain the specified string. FindList["file", {"text_1", "text_2", ...}] gives a list of all lines that ...

While the default settings for plots created in Mathematica are sufficient in most cases, nearly every aspect of plots is customizable. In addition to letting you change the ...

LibraryUnload[lib] unloads all functions that have been loaded from a Wolfram Library, then it unloads the library.

At the core of Mathematica's graphics language are geometrical objects, represented succinctly and efficiently by simple symbolic constructs —to which all of Mathematica's ...

ArrayQ[expr] gives True if expr is a full array or a SparseArray object, and gives False otherwise. ArrayQ[expr, patt] requires expr to be a full array with a depth that ...

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

Building on Mathematica's integrated symbolic architecture, it becomes easy to introduce powerful dynamic behavior into any aspect of visualization. Single Mathematica ...