Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

THIS important new Cambridge tract is concerned with the modern developments of the mathematical theory of Fourier series. The character of this theory was radically altered during the decade 1900–10 ...

A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which ...

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IN all expositions of Fourier's series which have come to my notice, it is expressly stated that the series can represent a discontinuous function.