PoincareSection is a setting for the option TrekGenerator that specifies that the Poincaré section for differential equations is used to generate treks.

A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a ...

A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

GaussianMatrix[r] gives a matrix that corresponds to a Gaussian kernel of radius r. GaussianMatrix[{r, \[Sigma]}] gives a matrix corresponding to a Gaussian kernel with ...

Normalize[v] gives the normalized form of a vector v. Normalize[z] gives the normalized form of a complex number z.Normalize[expr, f] normalizes with respect to the norm ...

One of the important features of Mathematica is its ability to give you exact, symbolic, results for computations. There are, however, computations where it is just ...

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...

Del[x] displays as \[Del]x.

The IDA package is part of the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) developed at the Center for Applied Scientific Computing of Lawrence ...