You can define wavelets to plug into the wavelet analysis framework by using the correct template. A wavelet wave is of the form wfam[args], where wfam is the symbol that ...

A typical Mathematica notebook containing text, graphics, and Mathematica expressions. The brackets on the right indicate the extent of each cell. Mathematica notebooks are ...

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

If you type in an expression like 0/0, Mathematica prints a message, and returns the result Indeterminate. An expression like 0/0 is an example of an indeterminate numerical ...

Matrix inversion. Here is a simple 2×2 matrix. This gives the inverse of m. In producing this formula, Mathematica implicitly assumes that the determinant ad-bc is nonzero.

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

Expressions corresponding to notebooks. Here is a simple Mathematica notebook. Here is the expression that corresponds to this notebook.

Pure functions. When you use functional operations such as Nest and Map, you always have to specify a function to apply. In all the examples above, we have used the "name" of ...

Mathematica always allows you to refer to special characters by using names such as ∖[Alpha] or explicit hexadecimal codes such as ∖:03b1. And when Mathematica writes out ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...