Fourier Analysis 2: Fourier Series of a 'broken' function

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.

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[illusion422]

Whats the point of fourier series, since most series we cannot find the sum?

[donylee]

Well, I'm certainly not an expert in Fourier series, but what I can say is this. Firstly, yes, we cannot explicitly write the sum to infinity. Still, it is substantial progress that we write a function in terms of trigonometry functions. This way, we can analyze otherwise complicating functions by looking at them in the perspective of cosine and sine functions, which them uses the results of frequency, amplitude, differentiate and integration etc.

[donylee]

Second, Fourier series is one of the ways which facilities writing a function FROM a piecewise continuous graph. This idea is important in modeling many phenomena in physics and engineering such as computing and the CAT scan diagnostic technique of modern medicine.

[alextuesday]

Good explanation indeed.. ive seen a few comments saying slow down but i think your speed is good as it allows us to recap the lecture without wasting time.. those who dont grasp every word, just rewind?

[AcousticSpade]

good pace, i only need to recap my knowledge on this stuff before exams...the less waffle the better

[nay1978miles]

This bloke thinks faster than he speaks...

[bur7ama1989]

After long hours of staring at the horrible examples from my Signals and Systems text book and reviewing class notes, I watched your video. It took me half an hour (including viewing time) to gain what I needed to know about Fourier Analysis. Your just as fast as my professor, but I can't rewind my professor. Thanks, keep it up.

[wrinklywitwicky]

this function is an even function right?

[mosaren]

i like your style, thank you :)

[sanetejas]

@ronalddlelariarte No he spoke in English. He said we are moving here using identity.

[sanetejas]

He is speaking fast but teaching slow........

[FurlowFurlow]

@alextuesday Yeah, but its to fast. If he dragged this out to 15 minuets it would only waste an extra 5 mins. Time isn't that scarce, but it would be a whole lot easier to follow.

[jstone98]

I love this guy! Great explainor.

[ronalddlelariarte]

at 5:58 to 6:01 he was speaking Chinese..

[Formslip]

at first i was like o wow hold on lightning speed i dont even...

then i watched it. you sir, are the leading teacher of the Fourier series on the interwebs, no lie.

i thank you. my knowledge has gone from "0" to "at least a little bit."