This is documentation for Mathematica 9, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced by new methods being discovered at Wolfram Research, the algorithms in Mathematica probably now reach almost every integral and differential equation for which a closed form can be found.


D () — partial derivatives of scalar or vector functions

Dt total derivatives

Integrate () symbolic integrals in one or more dimensions

Vector Calculus »

Grad ▪ Div ▪ Curl ▪ Laplacian ▪ ...

CoordinateChartData computations in curvilinear coordinates

Series power series and asymptotic expansions »

Limit limits

DSolve symbolic solutions to differential equations

Minimize, Maximize symbolic optimization

Sum, Product symbolic sums and products

Integral Transforms »

LaplaceTransform ▪ FourierTransform ▪ Convolve ▪ DiracDelta ▪ ...

Normalize, Orthogonalize normalize, orthogonalize families of functions

Numerical Calculus »

NIntegrate ▪ NDSolve ▪ NMinimize ▪ NSum ▪ ...

Differential Operator Functions »

Derivative symbolic and numerical derivative functions

DifferentialRoot general representation of linear differential solutions

Discrete Calculus »

DifferenceDelta ▪ GeneratingFunction ▪ RSolve ▪ RecurrenceTable ▪ ...