Ways to label two-dimensional plots. Here is a plot, using the default Axes->True. Setting Frame->True generates a frame with axes, and removes tick marks from the ordinary ...

You can enable logging in two ways. The log file records messages as they occur, building up a detailed record of license activity over a period of time. Logging supports ...

Whenever machine-precision numbers appear in a calculation, the whole calculation is typically done in machine precision. Mathematica will then give machine-precision numbers ...

Matrix inversion. Here is a simple 2×2 matrix. This gives the inverse of m. In producing this formula, Mathematica implicitly assumes that the determinant ad-bc is nonzero.

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) ...

NIntegrate Introduction NIntegrate Integration Strategies NIntegrate Integration Rules

[BerntEspGenz91] Berntsen, J., T. O. Espelid, and A. Genz. "An Adaptive Algorithm for the Approximate Calculation of Multiple Integrals." ACM Trans. Math. Softw. 17, no. 4 ...

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 ...

Pure functions. When you use functional operations such as Nest and Map, you always have to specify a function to apply. In all the examples above, we have used the "name" of ...