NestList (Built-in Mathematica Symbol)

NestList[f, expr, n] gives a list of the results of applying f to expr 0 through n times.

Attributes (Mathematica Tutorial)

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 ...

Basic Objects (Mathematica Tutorial)

Expressions are the main type of data in Mathematica. Expressions can be written in the form h[e_1,e_2,…]. The object h is known generically as the head of the expression. ...

Abel Equations (Mathematica Tutorial)

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 ...

Classification of Differential Equations (Mathematica Tutorial)

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

Functions with Sensitive Dependence on ... (Mathematica Tutorial)

Functions that are specified by simple algebraic formulas tend to be such that when their input is changed only slightly, their output also changes only slightly. But ...

Norms in NDSolve (Mathematica Tutorial)

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

Sparse Arrays: Manipulating Lists (Mathematica Tutorial)

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 ...

Using Assumptions (Mathematica Tutorial)

Mathematica normally makes as few assumptions as possible about the objects you ask it to manipulate. This means that the results it gives are as general as possible. But ...

Creating Tables (DatabaseLink Tutorial)

SQLCreateTable creates a new table in a database. An alternative, using raw SQL, is described in "Creating Tables with Raw SQL". If you find that the examples in this ...