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 ...

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

The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

On most computer systems, you can execute external programs or commands from within Mathematica. Often you will want to take expressions you have generated in Mathematica, ...

Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...

A common operation in analyzing various kinds of data is to find the discrete Fourier transform (or spectrum) of a list of values. The idea is typically to pick out ...

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 ...

You may have noticed that there are two different ways to make assignments in Mathematica: lhs=rhs and lhs:=rhs. The basic difference between these forms is when the ...

MathLM is available for Windows, Linux, and Mac OS X. For a detailed list of specific platforms, visit www.wolfram.com/mathematica/features/system-requirements.html. Each ...