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 

8/3/2023 1:04:28 PM