When you define a complicated function, you will often want to let some of the arguments of the function be "optional". If you do not give those arguments explicitly, you ...

The ability to define and use your own functions is part of what gives Mathematica such power. It is often inconvenient to have to explicitly name a function for every small ...

Module and With allow you to give a specific list of symbols whose names you want to treat as local. In some situations, however, you want to automatically treat certain ...

Using original algorithms developed at Wolfram Research, Mathematica evaluates error and exponential integral functions anywhere in the complex plane, to arbitrary ...

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...

When you make a function definition using :=, the value of the function is recomputed every time you ask for it. In some kinds of calculations, you may end up asking for the ...

 

x += dx adds dx to x and returns the new value of x.

In many practical situations it is convenient to consider limits in which a fixed amount of something is concentrated into an infinitesimal region. Ordinary mathematical ...

Finding and setting values of symbols. Mathematica effectively stores all definitions you give as lists of transformation rules. When a particular symbol is encountered, the ...