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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.


diff Differentiate symbolic expression or function
functionalDerivative Functional derivative
int Definite and indefinite integrals
rsums Interactive evaluation of Riemann sums
vpaintegral Numerical integration using variable precision
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
taylortool Taylor series calculator

Sums & Products

cumprod Symbolic cumulative product
cumsum Symbolic cumulative sum
symprod Product of series
symsum Sum of series
limit Compute limit of symbolic expression
fourier Fourier transform
ifourier Inverse Fourier transform
ilaplace Inverse Laplace transform
iztrans Inverse Z-transform
laplace Laplace transform
sympref Set symbolic preferences
ztrans Z-transform



Differentiate symbolic expressions and functions.


Integrate symbolic expressions and functions.

Taylor Series

Taylor series expansion of symbolic expressions and functions.

Fourier Transforms and Inverse

Fourier and Inverse Fourier transforms of symbolic expressions.

Solve Differential Equations Using Laplace Transform

Laplace and Inverse Laplace transforms of symbolic expressions and functions.

Z-Transform and Inverse

Z-Transforms and inverses of symbolic expressions and functions.

Symbolic Summation

Sum symbolic vectors, matrices, or symbolic series.

Padé Approximant

Pade approximant of symbolic expressions and functions.


Limits of symbolic expressions and functions.

Find Asymptotes, Critical and Inflection Points

Find minima, maxima, and asymptotes by using derivatives and limits.

Functional Derivatives Tutorial

Find functional derivatives, which are the derivative of a functional with respect to a function.

Featured Examples

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