General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

LeastSquares[m, b] finds an x that solves the linear least-squares problem for the matrix equation m.x == b.

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, ...

Integration functions. Here is the integral ∫_a^bx^2 dx. This gives the multiple integral ∫_0^adx ∫_0^bd y(x^2+y^2).

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

Functions that are specified by simple algebraic formulas tend to be such that when their input is changed only slightly, their output also changes only slightly. But ...

Directory[] gives the current working directory.

ParentDirectory[] gives the parent of the current working directory. ParentDirectory["dir"] gives the parent of the directory dir.

$HomeDirectory gives your "home" directory.