There are often many different ways to write the same algebraic expression. As one example, the expression (1+x)^2 can be written as 1+2x+x^2. Mathematica provides a large ...

The essence of most methods is in the local quadratic model that is used to determine the next step. The FindMinimum function in Mathematica has five essentially different ...

There are some close connections between finding a "local minimum" and solving a set of nonlinear equations. Given a set of n equations in n unknowns, seeking a solution r(x) ...

You can use lists as tables of values. You can generate the tables, for example, by evaluating an expression for a sequence of different parameter values. This gives a table ...

AmplitudeModulation[f_c, f_m, m_i, dur] creates a Sound object that is an amplitude-modulated sinusoid, having carrier and modulating frequencies f_c and f_m, measured in ...

Install["name"] starts a MathLink-compatible external program and installs Mathematica definitions to call functions in it.

PrimePowerQ[expr] yields True if expr is a power of a prime number, and yields False otherwise.

Reap[expr] gives the value of expr together with all expressions to which Sow has been applied during its evaluation. Expressions sown using Sow[e] or Sow[e, tag_i] with ...

Now that we have introduced the basic features of patterns in Mathematica, we can use them to give a more or less complete example. We will show how you could define your own ...

Some basic matrix operations. Transposing a matrix interchanges the rows and columns in the matrix. If you transpose an m×n matrix, you get an n×m matrix as the result. ...