The differential equations that arise in modern applications often have discontinuous coefficients. DSolve can handle a wide variety of such ODEs with piecewise coefficients. ...

A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a ...

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 ...