Mathematica: Calculus

Mathematica utilizes centuries of mathematical development, along with constantly updated methods discovered at Wolfram Research, into a small number of powerful functions and algorithms that are capable of reaching "almost every integral and differential equation of which a closed form can be found."

Below are a few examples of various commands used to evaluate calculus functions and algorithms:

D (PartialD) -- partial derivatives, of scalar or vector functions
Dt -- total derivatives
Integrate (Integral) -- 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 -- limit
DSolve -- symbolic solutions to differential equations
Minimize, Maximize -- symbolic optimization
Sum, Product -- symbolic sums and products

DifferenceQuotient — difference quotients

Integral Transforms:

Normalize, Orthogonalize -- normalize, orthogonalize families of functions

• LaplaceTransform
• FourierTransform
• Convolve
• DiracDelta....

Function Properties

• FunctionRange
• FunctionDomain
• FunctionPeriod

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
• Generating Function
• RSolve
• RecurrenceTable...

Referenced from: Mathematica