Calculus
TopicOverview »
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