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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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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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Another way of writing the Fourier Series of functions which are integrable on [0, L], is to do a half range expansion, this time with sine terms.
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This lessons deals with writing the Fourier Series of functions which are integrable on [0, L], in which case we will do a half range expansion, first forming a cosine series.
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Using a simple substitution, we extend the definition of a Fourier Series of a function, this time integrable from -L to L.
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NASA Destination Tomorrow Segment describing GIFTS (Geostationary Imaging Fourier Transform Spectrometer), the future of weather satellite technology which stands to aid in the understanding of weather processes, climate, atmospheric pollution, and severe.
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Using the techniques taught of getting the half range expansion of a function with either cosine or sine terms, we shall have a look at f(x)=e^2x on [0, 1].
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![Fourier Analysis 3: Fourier Series of function on [-L, L]](http://img.youtube.com/vi/M7HLT3cwJPI/2.jpg "Fourier Analysis 3: Fourier Series of function on [-L, L]")
