In calculus even more than other areas, the Wolfram Language 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 the Wolfram Language 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

ImplicitD implicit 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 directed and undirected limits, univariate and multivariate

MinLimit, MaxLimit lower and upper limits

DSolve symbolic solutions to differential equations

Minimize, Maximize symbolic optimization

Discrete Calculus »

Sum, Product symbolic sums and products

DifferenceQuotient  ▪  DifferenceDelta  ▪  DiscreteLimit  ▪  RSolve  ▪  ...

Numerical Calculus »

NIntegrate  ▪  NDSolve  ▪  NMinimize  ▪  NSum  ▪  ...

Asymptotic Calculus »

AsymptoticIntegrate  ▪  AsymptoticDSolveValue  ▪  AsymptoticSum  ▪  AsymptoticRSolveValue  ▪  ...

Integral Transforms »

LaplaceTransform  ▪  FourierTransform  ▪  Convolve  ▪  DiracDelta  ▪  ...

Normalize, Orthogonalize normalize, orthogonalize families of functions

Function Properties »

FunctionRange  ▪  FunctionDomain  ▪  FunctionInjective  ▪  FunctionPeriod  ▪  ...

Calculus & Geometry »

ArcLength  ▪  Area  ▪  Volume  ▪  RegionDistance  ▪  ...

Differential Operator Functions »

Derivative symbolic and numerical derivative functions

DifferentialRoot general representation of linear differential solutions

DSolveChangeVariables change of variables in differential equations

IntegrateChangeVariables change of variables in integrals