Internal representations used by Mathematica. When you type input into Mathematica, a data structure is created in the memory of your computer to represent the expression you ...

Manipulate Introduction to Control Objects Views

This equation is solved by simply integrating the right-hand side with respect to x. Here is a plot of the integral curves for different values of the arbitrary constant C[1].

Sign[x] gives -1, 0, or 1 depending on whether x is negative, zero, or positive.

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NDSolve solves a differential equation numerically. It returns solutions in a form that can be readily used in many different ways. One typical use would be to produce a plot ...

Play[f, {t, t_min, t_max}] creates an object that plays as a sound whose amplitude is given by f as a function of time t in seconds between t_min and t_max.

Precision[x] gives the effective number of digits of precision in the number x.

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...