When you manipulate power series, it is sometimes convenient to think of the series as representing functions, which you can, for example, compose or invert. Composition and ...

Mathematica provides various ways to set up conditionals, which specify that particular expressions should be evaluated only if certain conditions hold. Conditional ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

Mathematica allows you not only to export graphics and sounds, but also to import them. With Import you can read graphics and sounds in a wide variety of formats, and bring ...

Just as the equation x^2+3x==2 asserts that x^2+3x is equal to 2, so also the inequality x^2+3x>2 asserts that x^2+3x is greater than 2. In Mathematica, Reduce works not only ...

Finding memory usage. Particularly for symbolic computations, memory is usually the primary resource which limits the size of computations you can do. If a computation runs ...

You can use the keyboard to move the cursor forward or backward one character or one word at a time. You can also delete the character or word to the right or the left of the ...

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...