The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

Solving linear first-order ODEs is straightforward and only requires the use of a suitable integrating factor. In sharp contrast, there are a large number of methods ...

Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary ...

A very common batch processing task is to reduce the dimensions of a set of images in one or more system folders, in effect constructing thumbnail images. Mathematica 's file ...

The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to ...

The hierarchy of levels at which options can be set. Here is a notebook containing three cells. This is what happens when the setting CellFrame->True is made specifically for ...

The introduction of Mathematica 6 in 2007 represented a revolutionary redefinition of Mathematica. Arriving only 18 months after Mathematica 6, Mathematica 7 represents ...

In addition to the interfaces of Import and Export, Mathematica 8 comes with an autoloading mechanism that simplifies the registration of formats used by the Import and ...

You can tell a lot about what "type" of expression something is by looking at its head. Thus, for example, an integer has head Integer, while a list has head List. In a ...

Ways to get pieces of matrices. Matrices in Mathematica are represented as lists of lists. You can use all the standard Mathematica list-manipulation operations on matrices. ...