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 ...

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

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 ...

Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...

Lists are normally specified in Mathematica just by giving explicit lists of their elements. But particularly in working with large arrays, it is often useful instead to be ...

Widgets created within a user interface definition can be named and registered in an object registry for easy lookup reference by script code and other widgets. Complete ...

NLimit[expr, z -> z_0] numerically finds the limiting value of expr as z approaches z_0.

BSplineCurve[{pt_1, pt_2, ...}] is a graphics primitive that represents a non-uniform rational B-spline curve with control points pt_i.