Combinatorial functions. The factorial function n! gives the number of ways of ordering n objects. For non-integer n, the numerical value of n! is obtained from the gamma ...

If you make a definition like f[x_]:=x Sin[x], Mathematica will store the expression x Sin[x] in a form that can be evaluated for any x. Then when you give a particular value ...

You can enter complex numbers in Mathematica just by including the constant I, equal to Sqrt[-1]. Make sure that you type a capital I. If you are using notebooks, you can ...

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient search methods use ...

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, ...

Convolution and correlation are central to many kinds of operations on lists of data. They are used in such areas as signal and image processing, statistical data analysis, ...

Whenever Mathematica draws a three-dimensional object, it always effectively puts a cuboidal box around the object. With the default option setting Boxed->True, Mathematica ...

When you set up a graphics object in Mathematica, you give coordinates for the various graphical elements that appear. When Mathematica renders the graphics object, it has to ...

There are many situations where one wants to find a formula that best fits a given set of data. One way to do this in Mathematica is to use Fit. Basic linear fitting. Here is ...