based on an earlier version of the Wolfram Language.
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
CoordinateChartData — computations in curvilinear coordinates
Limit — limits
DSolve — symbolic solutions to differential equations
Derivative — symbolic and numerical derivative functions
DifferentialRoot — general representation of linear differential solutions