This is documentation for Mathematica 8, 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
Series power series and asymptotic expansions »
Limit limits
DSolve symbolic solutions to differential equations
Minimize, Maximize symbolic optimization
Sum, Product symbolic sums and products
Normalize, Orthogonalize normalize, orthogonalize families of functions
NIntegrate  ▪ NDSolve  ▪ NMinimize  ▪ NSum  ▪ ...
Derivative symbolic and numerical derivative functions
DifferentialRoot general representation of linear differential solutions