Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

Mathematica provides various ways to set up conditionals, which specify that particular expressions should be evaluated only if certain conditions hold. Conditional ...

Convolution and correlation are central to many kinds of operations on lists of data. They are used in such areas as signal and image processing, statistical data analysis, ...

In addition to its graphical results, Wolfram|Alpha can provide alternative representations that contain additional information or are well suited to particular tasks. These ...

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

Implicit Runge–Kutta methods have a number of desirable properties. The Gauss–Legendre methods, for example, are self-adjoint, meaning that they provide the same solution ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

Lists are normally specified in Mathematica just by giving explicit lists of their elements. But particularly in working with large arrays, it is often useful instead to be ...

Mathematica uses various syntactic rules to interpret input that you give, and to convert strings and boxes into expressions. The version of these rules that is used for ...