Xor[e_1, e_2, ...] is the logical XOR (exclusive OR) function. It gives True if an odd number of the e_i are True, and the rest are False. It gives False if an even number of ...

MedianFilter[image, r] filters image by replacing every value by the median in its range r neighborhood. MedianFilter[data, r] applies median filtering to an array of data.

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Mathematica usually goes about its work silently, giving output only when it has finished doing the calculations you asked for. However, if it looks as if Mathematica is ...

Trig is an option for various polynomial manipulation functions that specifies whether trigonometric functions should be treated like polynomial elements.

Converting power series to normal expressions. Power series in Mathematica are represented in a special internal form, which keeps track of such attributes as their expansion ...

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 ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathematica function NDSolve, on the other hand, is a general numerical differential ...