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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Limits, Differentiation, and Integration

`limit`	Limit of symbolic expression
`diff`	Differentiate symbolic expression or function
`functionalDerivative`	Functional derivative
`int`	Definite and indefinite integrals
`vpaintegral`	Numerical integration using variable precision

Vector Analysis

`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

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

Transforms

`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

Interactive Tools

`funtool`	Function calculator
`rsums`	Interactive evaluation of Riemann sums
`taylortool`	Taylor series calculator

Topics

Differentiation

Differentiate symbolic expressions and functions.

Create Symbolic Functions

Use symbolic functions that accept symbolic inputs, such as f(x,y).

Integration

Integrate symbolic expressions and functions.

Taylor Series

Taylor series expansion of symbolic expressions and functions.

Fourier and Inverse Fourier Transforms

Fourier and inverse Fourier transforms of symbolic expressions.

Solve Differential Equations Using Laplace Transform

Laplace and Inverse Laplace transforms of symbolic expressions and functions.

Solve Difference Equations Using Z-Transform

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

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

Learn Calculus in the Live Editor

Learn calculus and applied mathematics using the Symbolic Math Toolbox™. The example shows introductory functions fplot and diff.

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Differentiation

Analytically find and evaluate derivatives using Symbolic Math Toolbox™. In the example you will find the 1st and 2nd derivative of f(x) and use these derivatives to find local maxima, minima and inflection points.

Open Live Script