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

Special forms for some common symbols. This is equivalent to Sin[60Degree]. Here is the long form of the input.

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 ...

Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...

A common operation in analyzing various kinds of data is to find the discrete Fourier transform (or spectrum) of a list of values. The idea is typically to pick out ...

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 ...

The way modules work in Mathematica is basically very simple. Every time any module is used, a new symbol is created to represent each of its local variables. The new symbol ...

You may have noticed that there are two different ways to make assignments in Mathematica: lhs=rhs and lhs:=rhs. The basic difference between these forms is when the ...

Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...