# Calculus

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

## 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.