Main Content


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.


expand all

limitLimit of symbolic expression
diffDifferentiate symbolic expression or function
functionalDerivativeFunctional derivative (variational derivative)
intDefinite and indefinite integrals
vpaintegralNumerical integration using variable precision
changeIntegrationVariableIntegration by substitution (Since R2019b)
integrateByPartsIntegration by parts (Since R2019b)
releaseEvaluate integrals (Since R2019b)
curlCurl of symbolic vector field
divergenceDivergence of symbolic vector field
gradientGradient vector of symbolic scalar field
hessianHessian matrix of symbolic scalar function
jacobianJacobian matrix of symbolic function
laplacianLaplacian of symbolic field
potentialPotential of vector field
vectorPotentialVector potential of vector field

Series Expansions

padePade approximant
rsumsInteractive evaluation of Riemann sums
seriesPuiseux series
taylorTaylor series

Sums & Products

cumprodSymbolic cumulative product
cumsumSymbolic cumulative sum
symprodProduct of series
symsumSymbolic sum of series
vpasumNumerical summation using variable precision (Since R2020b)
fourierFourier transform
ifourierInverse Fourier transform
htransHilbert transform
ihtransInverse Hilbert transform
laplaceLaplace transform
ilaplaceInverse Laplace transform
iztransInverse Z-transform
symprefSet symbolic preferences
pdeCoefficientsExtract coefficients of partial differential equation (Since R2021a)
pdeCoefficientsToDoubleConvert symbolic PDE coefficients to double format (Since R2021a)
funtoolFunction calculator
rsumsInteractive evaluation of Riemann sums
taylortoolTaylor series calculator