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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 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
 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
 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.

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

Mathematical Modeling with Symbolic Math Toolbox

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