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Numerical Integration and Differentiation

Quadratures, double and triple integrals, and multidimensional derivatives

Numerical integration functions can approximate the value of an integral whether or not the functional expression is known:

  • When you know how to evaluate the function, you can use integral to calculate integrals with specified bounds.

  • To integrate an array of data where the underlying equation is unknown, you can use trapz, which performs trapezoidal integration using the data points to form a series of trapezoids with easily computed areas.

For differentiation, you can differentiate an array of data using gradient, which uses a finite difference formula to calculate numerical derivatives. To calculate derivatives of functional expressions, you must use Symbolic Math Toolbox™.


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integralNumerical integration
integral2Numerically evaluate double integral
integral3Numerically evaluate triple integral
quadgkNumerically evaluate integral — Gauss-Kronrod quadrature
quad2dNumerically evaluate double integral — tiled method
cumtrapzCumulative trapezoidal numerical integration
trapzTrapezoidal numerical integration
del2Discrete Laplacian
diffDifferences and approximate derivatives
gradientNumerical gradient
polyintPolynomial integration
polyderPolynomial differentiation