Mathematica: Calculus

There may be broken links in this article, the GROK staff has been notified and is working to resolve the issue.

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
  • RecurranceTable...


Referenced from: Mathematica 

6/19/2019 1:18:53 PM