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<title>Fourier Analysis Online Course,  Other</title>
<link>http://freevideolectures.com</link>
<description><![CDATA[A study of the great work by mathematician Jospeh Fourier (1768 - 1830). I present to you a module of Fourier Analysis. Fourier Analysis Online Course,  Other. Subscribed to the feed and get updated]]></description>
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<title>Lecture 1: Fourier Analysis 1: Definition of the Fourier Series</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/1</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 2: Fourier Analysis 2: Fourier Series of a 'broken' function</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/2</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 3: Fourier Analysis 3: Fourier Series of function on [-L, L]</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/3</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[Using a simple substitution, we extend the definition of a Fourier Series of a function, this time integrable from -L to L.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 4: Fourier Analysis 4: Example of Fourier Series on [-L, L]</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/4</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[With our definitions of a Fourier Series on [-L, L], let us look at a simple example, this time a function integrable on [-3, 3].

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 5: Fourier Analysis 5: Fourier Series on odd and even functions</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/5</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 6: Fourier Analysis 6: Fourier Series of x^2 [MAY NOT = f(x)]</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/6</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 7: Fourier Analysis 7: Recap on piecewise continuous functions</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/7</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[We will revise some basic definitions of limits and derivatives of piecewise continuous functions which are needed in learning the convergence theorem of Fourier Series.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 8: Fourier Analysis 8: Convergence Theorem of a Fourier Series</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/8</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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).

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 9: Fourier Analysis 9: Convergence of Fourier Series of f(x)=2x</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/9</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[Using the convergence theorem, we have another looking at the Fourier Series of a simple function f(x) = 2x on [-pi, pi].

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 10: Fourier Analysis 10: Convergence of a 'broken' function</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/10</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[We shall look at a slightly more complicated example. Where does the Fourier Series of a 'broken' function converge to.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 11: Fourier Analysis 11: Graphs of various Fourier Series</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/11</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 12: Fourier Analysis 12: Contrasting Power and Fourier series</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/12</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[After studying the convergence theorem, we will now compare that with another convergence theorem we know, that being the one for the Power Series.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 13: Fourier Analysis 13: Fourier Cosine Series</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/13</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 14: Fourier Analysis 14: Fourier Sine Series</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/14</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 15: Fourier Analysis 15: Half range expansions of f(x)=e^2x</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/15</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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].

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 16: Fourier Analysis 16: Periodic Functions</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/16</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[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.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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<title>Lecture 17: Fourier Analysis 17: Phase Angle form of a function</title>
<link>http://freevideolectures.com/Course/2616/Fourier-Analysis/17</link>
<pubDate>Fri, 15 Oct 2010 00:00:00 -0600</pubDate>
<description><![CDATA[We find the Fourier Series of a periodic function g(x), write it in its phase angle form and glimpse at its amplitude spectrum.

Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.]]></description>
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</channel>
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