Consider the matrix differential equation where the initial value y_0 y(0)∈^m×p is given. Assume that y_0^Ty_0I, that the solution has the property of preserving ...

In some cases it is useful to split the differential system into subsystems and solve each subsystem using appropriate integration methods. Recombining the individual ...

NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

The Mathematica function NIntegrate is a general numerical integrator. It can handle a wide range of one-dimensional and multidimensional integrals. Finding a numerical ...

The function NDSolve discussed in "Numerical Differential Equations" allows you to find numerical solutions to differential equations. NDSolve handles both single ...

With <<, you can read files that contain Mathematica expressions given in input form. Sometimes, however, you may instead need to read files of data in other formats. For ...

Formatting lists as tables and matrices. Here is a list. Grid gives the list typeset in a tabular format.

Tensors are mathematical objects that give generalizations of vectors and matrices. In Mathematica, a tensor is represented as a set of lists, nested to a certain number of ...

For minimization problems for which the objective function is a sum of squares, it is often advantageous to use the special structure of the problem. Time and effort can be ...

The utility functions FindMinimumPlot and FindRootPlot show search data for FindMinimum and FindRoot for one- and two-dimensional functions. They work with essentially the ...