If you have a function defined in an external program, then what you need to do in order to make it possible to call the function from within Mathematica is to add ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using ...

The names of built-in functions follow some general guidelines. The main expression or object on which a built-in function acts is usually given as the first argument to the ...

Built into Mathematica are a large number of special characters intended for use in mathematical and other notation. "Listing of Named Characters" gives a complete listing. ...

Files and pipes are both examples of general Mathematica objects known as streams. A stream in Mathematica is a source of input or output. There are many operations that you ...

In any interactive session, Mathematica effectively operates in a loop. It waits for your input, processes the input, prints the result, then goes back to waiting for input ...

The basis for a nonlinear conjugate gradient method is to effectively apply the linear conjugate gradient method, where the residual is replaced by the gradient. A model ...

Newton's method for nonlinear equations is based on a linear approximation so the Newton step is found simply by setting M_k(p)=0, Near a root of the equations, Newton's ...

When large amounts of data are being transferred between Mathematica and a database, you may find that the operations are slow. In this case it may be advantageous to use a ...