The Mathematica kernel provides the functions FourierTransform and InverseFourierTransform for computing the symbolic Fourier exponential transform and inverse transform. It ...

MatrixPower[m, n] gives the n\[Null]\[Null]^th matrix power of the matrix m. MatrixPower[m, n, v] gives the n\[Null]^th matrix power of the matrix m applied to the vector v.

RootApproximant[x] converts the number x to one of the "simplest" algebraic numbers that approximates it well.RootApproximant[x, n] finds an algebraic number of degree at ...

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

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 ...

ND[expr, x, x_0] gives a numerical approximation to the derivative of expr with respect to x at the point x_0.ND[expr, {x, n}, x_0] gives a numerical approximation to the ...

DiracDelta[x] represents the Dirac delta function \[Delta](x). DiracDelta[x_1, x_2, ...] represents the multidimensional Dirac delta function \[Delta](x_1, x_2, ...).

LiftingFilterData[...] represents lifting-filter data used to compute forward and inverse lifting wavelet transforms.

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

Mathematica has over 3000 built-in functions and other objects, all based on a single unified framework, and all carefully designed to work together, both in simple ...