A Riccati equation is a first-order equation of the form This equation was used by Count Riccati of Venice (1676–1754) to help in solving second-order ordinary differential ...

If you use the notebook front end for Mathematica, then you can enter some of the operations discussed here in special ways. Special and ordinary ways to enter mathematical ...

Dt[f, x] gives the total derivative d f/d x. Dt[f] gives the total differential d f. Dt[f, {x, n}] gives the multiple derivative d^n f/d x^n. Dt[f, x_1, x_2, ...] gives d/d ...

MatrixRank[m] gives the rank of the matrix m.

lhs != rhs or lhs != rhs returns False if lhs and rhs are identical.

Mathematica is to its core a fundamentally extensible system, in which efficient, modular, reusable packages of any size can readily be created. Mathematica's symbolic ...

Mathematica provides several convenient methods for extracting and manipulating parts of matrices. The flexible [[ ]] (Part) and ;; (Span) syntaxes provide compact yet ...

Input from Above copies and pastes contents of the nearest preceding input cell.

ActiveStyle is an option for Hyperlink and related constructs that specifies styles to add when the constructs are active, typically as a result of the mouse being over them.

AlphaChannel[image] returns the alpha channel of image.