# 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 `integrateByParts` Integration by parts `release` Evaluate integrals
 `curl` Curl of vector field `divergence` Divergence of vector field `gradient` Gradient vector of scalar function `hessian` Hessian matrix of scalar function `jacobian` Jacobian matrix `laplacian` Laplacian of scalar function `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` Sum of series `vpasum` Numerical summation using variable precision
 `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 `pdeCoefficientsToDouble` Convert symbolic PDE coefficients to `double` format
 `funtool` Function calculator `rsums` Interactive evaluation of Riemann sums `taylortool` Taylor series calculator