When you manipulate power series, it is sometimes convenient to think of the series as representing functions, which you can, for example, compose or invert. Composition and ...

Systems of ODEs are important in various fields of science, such as the study of electricity and population biology. Like single ODEs, systems of ODEs can classified as ...

Built on powerful and elegant principles, the core Mathematica language has emerged over the past 20 years as perhaps the world's richest and deepest programming language. ...

StateSpaceModel[{a, b, c, d}] represents the state-space model with state matrix a, input matrix b, output matrix c, and transmission matrix d. StateSpaceModel[tf] gives a ...

Mathematica's uniform representation of vectors and matrices as lists automatically extends to tensors of any rank, allowing Mathematica's powerful list manipulation ...

The numerical method of lines is a technique for solving partial differential equations by discretizing in all but one dimension, and then integrating the semi-discrete ...

Mathematica has efficient systemwide 16-bit Unicode support, allowing a full range of international, technical and other character sets and character encodings.

For many kinds of practical calculations, the only operations you will need to perform on polynomials are essentially structural ones. If you do more advanced algebra with ...

Any combination of equations or inequalities can be thought of as implicitly defining a region in some kind of space. The fundamental function of Reduce is to turn this type ...

When you give a list of equations to Solve, it assumes that you want all the equations to be satisfied simultaneously. It is also possible to give Solve more complicated ...