If you have a list of elements, it is often important to be able to apply a function separately to each of the elements. You can do this in Mathematica using Map. This ...

It is always a good idea to give variables and functions names that are as explicit as possible. Sometimes, however, such names may get inconveniently long. In Mathematica, ...

Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

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 ...

Mathematica expressions provide a very general way to handle all kinds of data, and you may sometimes want to use such expressions inside your external programs. A language ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

Mathematica provides users with access to their computer's file system (Files), interprocess communication (MathLink Mathematica Functions), evaluation of data as code ...

Complicated algebraic expressions can usually be written in many different ways. Mathematica provides a variety of functions for converting expressions from one form to ...

This example demonstrates various techniques for designing a progress bar dialog and a number of options available to wrap the reusable widget involved. Here is one technique ...