The Music of the Primes..............goes on to say that Joe F would have recognized R's equation for the exact number of primes under a given number as the sums of waves..................and that not only was this mathematical modeling but the very physics of music were waves........like heat propagation...........one of the things Joe F was studying.........................

Electromagnetism..........................radiation........................are graphed as waves...........the color spectrum............

F]CHAPTER 4 FOURIER SERIES AND INTEGRALS

math.mit.edu/cse/websections/cse41.pdf

Square waves (1 or 0 or −1) are great examples, with delta functions in the ... portance of the decay rate) then the sum S(x) will inherit all three properties:.

Fourier series - Wikipedia

https://en.wikipedia.org/wiki/Fourier_series

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic ...

[PDF]Fourier Series - Stewart Calculus

www.stewartcalculus.com/data/.../upfiles/topics/6et_at_01_fs_stu.pdf

In Example 1 we found the Fourier series of the square-wave function, but we don't .... FIGURE 2 Partial sums of the Fourier series for the square-wave function.

[PDF]3. Fourier analysis

www.people.fas.harvard.edu/~djmorin/waves/Fourier.pdf

Nov 28, 2009 - written as a discrete sum of trigonometric or exponential functions ... Fourier transform: A general function that isn't necessarily periodic (but that ...

Fourier Series--Square Wave -- from Wolfram MathWorld

mathworld.wolfram.com › Calculus and Analysis › Series › Fourier Series

by EW Weisstein - ‎2003 - ‎Cited by 7 - ‎Related articles

DOWNLOAD Mathematica Notebook FourierSeriesSquareWave. Consider a square wave f(x) of length 2L . ... is the Heaviside step function. Since f(x)=f(2L-x) ..