The method can also be extended to multiple integrals.

Additionally, multiple integrals are used in many applications in physics.

Variational problems that involve multiple integrals arise in numerous applications.

Existence theorems for optimal control problems involving multiple integrals.

In electromagnetism, Maxwell's equations can be written using multiple integrals to calculate the total magnetic and electric fields.

The exponent is built up as an infinite series whose terms involve multiple integrals and nested commutators.

Main analysis theorems that relate multiple integrals:

Computed solutions of complicated difficult multiple integrals, using the distribution of the Correlation Coefficient.

The multiple integrals are a repeated convolution of this Gaussian G with copies of itself at adjacent times.

One important property of multiple integrals is that the value of an integral is independent of the order of integrands under certain conditions.

Working for Karl Pearson, F. N. David computed solutions to complicated multiple integrals, and the distribution of the correlation coefficients.

The multinomial probit model has as a disadvantage that it makes calculation of maximum likelihood infeasible for more than five alternatives as it involves multiple integrals.

Multiple integrals have many properties common to those of integrals of functions of one variable (linearity, commutativity, monotonicity, and so on.)

Smirnov's principal works in mathematical statistics and probability theory are devoted to the investigation of limit distributions by means of the asymptomatic behaviour of multiple integrals as the multiplicity is increased with limit.

The resolution of problems with multiple integrals consists, in most of cases, of finding a way to reduce the multiple integral to an iterated integral, a series of integrals of one variable, each being directly solvable.

He is author of several treatises, including one on the solution of numeric equations with multiple unknowns (1842); one on multiple integrals and their integrability conditions; one on the determination of the orbits of the comets.

In calculus, interchange of the order of integration is a methodology that transforms iterated integrals (or multiple integrals through the use of Fubini's theorem) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed.