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# Calculus

Symbolic differentiation, integration, series operations, limits, and transforms

Using Symbolic Math Toolbox™, you can differentiate and integrate symbolic expressions, perform series expansions, find transforms of symbolic expressions, and perform vector calculus operations by using the listed functions.

When modeling your problem, use assumptions to return the right results. See Use Assumptions on Symbolic Variables. To simplify your results, see Simplify Symbolic Expressions.

## Functions

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 `limit` Limit of symbolic expression `diff` Differentiate symbolic expression or function `functionalDerivative` Functional derivative (variational derivative) `int` Definite and indefinite integrals `vpaintegral` Numerical integration using variable precision `changeIntegrationVariable` Integration by substitution (Since R2019b) `integrateByParts` Integration by parts (Since R2019b) `release` Evaluate integrals (Since R2019b)
 `curl` Curl of symbolic vector field `divergence` Divergence of symbolic vector field `gradient` Gradient vector of symbolic scalar field `hessian` Hessian matrix of symbolic scalar function `jacobian` Jacobian matrix of symbolic function `laplacian` Laplacian of symbolic field `potential` Potential of vector field `vectorPotential` Vector potential of vector field

#### Series Expansions

 `pade` Pade approximant `rsums` Interactive evaluation of Riemann sums `series` Puiseux series `taylor` Taylor series

#### Sums & Products

 `cumprod` Symbolic cumulative product `cumsum` Symbolic cumulative sum `symprod` Product of series `symsum` Symbolic sum of series `vpasum` Numerical summation using variable precision (Since R2020b)
 `fourier` Fourier transform `ifourier` Inverse Fourier transform `htrans` Hilbert transform `ihtrans` Inverse Hilbert transform `laplace` Laplace transform `ilaplace` Inverse Laplace transform `ztrans` Z-transform `iztrans` Inverse Z-transform `sympref` Set symbolic preferences
 `pdeCoefficients` Extract coefficients of partial differential equation (Since R2021a) `pdeCoefficientsToDouble` Convert symbolic PDE coefficients to `double` format (Since R2021a)
 `funtool` Function calculator `rsums` Interactive evaluation of Riemann sums `taylortool` Taylor series calculator