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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 . to simplify your results, see .

functions

limit of symbolic expression
diffdifferentiate symbolic expression or function
functional derivative (variational derivative)
intdefinite and indefinite integrals
numerical integration using variable precision
integration by substitution
integration by parts
evaluate integrals
curl of symbolic vector field
divergence of symbolic vector field
gradient vector of symbolic scalar field
hessian matrix of symbolic scalar function
jacobian matrix of symbolic function
laplacian of symbolic field
potential of vector field
vector potential of vector field

series expansions

pade approximant
interactive evaluation of riemann sums
puiseux series
taylor series

sums & products

symbolic cumulative product
symbolic cumulative sum
product of series
symbolic sum of series
numerical summation using variable precision
fourier transform
inverse fourier transform
hilbert transform
inverse hilbert transform
laplace transform
inverse laplace transform
z-transform
inverse z-transform
set symbolic preferences
extract coefficients of partial differential equation
convert symbolic pde coefficients to double format
function calculator
interactive evaluation of riemann sums
taylor series calculator

topics

  • differentiation

    differentiate symbolic expressions and functions.


  • use symbolic functions that accept symbolic inputs for analytical calculations.

  • integration

    integrate symbolic expressions and functions.


  • taylor series expansion of symbolic expressions and functions.


  • fourier and inverse fourier transforms of symbolic expressions.


  • solve differential equations of an rlc circuit by using laplace and inverse laplace transforms.


  • z-transforms and inverses of symbolic expressions and functions.


  • sum symbolic vectors, matrices, or symbolic series.


  • pade approximant of symbolic expressions and functions.


  • limits of symbolic expressions and functions.


  • find minima, maxima, and asymptotes by using derivatives and limits.


  • this example shows how to use functional derivatives in symbolic math toolbox using the context of a wave equation.

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