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podjackel
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Homework Statement
#35 on this page
Homework Equations
Integral of a series can be assumed to be the sum of integrals
The Attempt at a Solution
Picture of Work
I am not sure where to proceed from here, advice?
R136a1 said:Try to explicitely calculate
[tex]\int_0^\lambda A_n \cos(\frac{2\pi n}{\lambda}x)dx[/tex]
A Fourier Series is a mathematical representation of a periodic function as a sum of sines and cosines. It is used to approximate any periodic function by breaking it down into simpler components.
The coefficients in a Fourier Series represent the amplitude of each sine and cosine term in the series. These coefficients are calculated using integrals of the periodic function over one period.
By finding the Fourier Series coefficients, we can approximate any periodic function with a finite number of terms. This is useful in many applications, such as signal processing and data compression.
The Fourier Series coefficients can be calculated using the Fourier Series formula, which involves taking integrals of the periodic function over one period. Alternatively, they can also be calculated using complex exponential functions.
Yes, the Fourier Series coefficients are unique for a given periodic function. This means that there is only one set of coefficients that can be used to represent a specific periodic function as a sum of sines and cosines.