In mathematical analysis , an integral transform useful in solving certain types of partial differential equations .
A function's Fourier transform is derived by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from - 221E; to + 221E; . The Fourier transform of a function g is given by
. Such transforms, discovered by Joseph Fourier , are particularly useful in studying problems concerning electrical potential.