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) ...

Searching for local minima and maxima. This finds the value of x which minimizes Γ(x), starting at x2. The last element of the list gives the value at which the minimum is ...

Derivatives in Mathematica work essentially the same as in standard mathematics. The usual mathematical notation, however, often hides many details. To understand how ...

When searching for a real simple root of a real valued function, it is possible to take advantage of the special geometry of the problem, where the function crosses the axis ...

A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: ...

This tutorial covers advanced features of the Manipulate command. It assumes that you have read "Introduction to Manipulate" and thus have a good idea what the command is for ...

This loads packages containing some test problems and utility functions. One of the first and simplest methods for solving initial value problems was proposed by Euler: ...

The Mathematica function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some ...

ReliefPlot[array] generates a relief plot of an array of height values.

SmoothDensityHistogram[{{x_1, y_1}, {x_2, y_2}, ...}] plots a smooth kernel histogram of the values {x_i, y_i}.SmoothDensityHistogram[{{x_1, y_1}, {x_2, y_2}, ...}, espec] ...