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 ...

Special forms for some common symbols. This is equivalent to Sin[60Degree]. Here is the long form of the input.

With the default option setting Lighting->Automatic, Mathematica uses a simulated lighting model to determine how to color polygons in three-dimensional graphics. Mathematica ...

You can use lists as tables of values. You can generate the tables, for example, by evaluating an expression for a sequence of different parameter values. This gives a table ...

The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...

All textual and graphical forms in Mathematica are ultimately represented in terms of nested collections of boxes. Typically the elements of these boxes correspond to objects ...

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 contains some powerful primitives for making structural changes to expressions. You can use these primitives both to implement mathematical properties such as ...

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.

Vectors and matrices in Mathematica are simply represented by lists and by lists of lists, respectively. The representation of vectors and matrices by lists. This is a 2×2 ...