Fourier Analysis 1 Definition of the Fourier We begin our study on the work of Joseph Fourier (1768-1830) with the definition of the Fourier Series - a way of expressing functions as infinite sums or integrals or trigonometry functions
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Fourier Analysis 11 Graphs of various Fourier Let's look at the graphs of various Fourier Series To illustrate the series, we will be taking the Nth partial sum It is also here where we notice some interesting behaviour of some Fourier Series
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Fourier Analysis 8 Convergence Theorem of a F A discussion on the Convergence Theorem of a Fourier Series, a very important theorem in Fourier Analysis How do we know when the Fourier Series converges to the function f(x)
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Fourier Analysis 6 Fourier Series of x^2 [MAY Using the even property of a function, we'll find the Fourier Series of x^2 on [-3, 3] which serves as a example of why certain functions NEED NOT agree with its Fourier Series A Convergence theorem is needed
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Fourier Analysis 5 Fourier Series on odd and We shall take advantage of certain properties of odd and even functions to simplify our work in finding the Fourier Series
ERRATA For odd functions, -f(x)=f(-x) Apologies for the mistake
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Fourier Analysis 2 Fourier Series of a 'broke Using our previous definitions, here is an example of how you write a Fourier Series from a graph of a function, a 'broken' function in this case
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Fourier Analysis 16 Periodic Functions We now extend the basic ideas we have of Fourier Series and look at a periodic functions, ones which repeats itself after a period T
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