# Documentation

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# Numerical Integration and Differentiation

Quadratures, double and triple integrals, and multidimensional derivatives

## Functions

 `integral` Numerical integration `integral2` Numerically evaluate double integral `integral3` Numerically evaluate triple integral `quadgk` Numerically evaluate integral, adaptive Gauss-Kronrod quadrature `quad2d` Numerically evaluate double integral, tiled method `cumtrapz` Cumulative trapezoidal numerical integration `trapz` Trapezoidal numerical integration `polyint` Polynomial integration
 `del2` Discrete Laplacian `diff` Differences and Approximate Derivatives `gradient` Numerical gradient `polyder` Polynomial differentiation

## Topics

Integration to Find Arc Length

This example shows how to parametrize a curve and compute the arc length using `integral`.

Complex Line Integrals

This example shows how to calculate complex line integrals using the `'Waypoints'` option of the `integral` function.

Singularity on Interior of Integration Domain

This example shows how to split the integration domain to place a singularity on the boundary.

Analytic Solution to Integral of Polynomial

This example shows how to use the `polyint` function to integrate polynomial expressions analytically.

Integration of Numeric Data

This example shows how to integrate a set of discrete velocity data numerically using `trapz` to approximate the total distance traveled.

Calculate Tangent Plane to Surface

This example shows how to approximate gradients of a function by finite differences.