StringSplit["string"] splits " string" into a list of substrings separated by whitespace. StringSplit["string", patt] splits into substrings separated by delimiters matching ...

When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...

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

The functions described here are among the most commonly used discrete univariate statistical distributions. You can compute their densities, means, variances, and other ...

Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

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

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 ( ...

Patterns are used throughout Mathematica to represent classes of expressions. A simple example of a pattern is the expression f[x_]. This pattern represents the class of ...

Functions for creating power series. Here is the power series expansion for exp(x) about the point x0 to order x^4. Here is the series expansion of exp(x) about the point ...