Fourier Series Part 2

Joseph Fourier developed a method for modeling any function with a combination of sine and cosine functions. You can graph this with your calculator easily and watch the modeling in action. Make sure you're in radian mode and let c=1:
f(x) = 4/(pi)*sin(x) + 4/(3pi)*sin(3x) + 4/(5pi)*sin(5x) + 4/(7pi)*sin(7x) + 4/(9pi)*sin(9x) + 4/(11pi)*sin(11x)

[kieransimcox]

Switched to 1080p to admire the beard to its fullest

[antoniussugianto]

This is exactly what i need... Fourier series explained in mathematical sense and not in physical sense.. thank you : )

[laurenkearley]

The GPA of everyone in my intro to signal processing class will forever be grateful for your videos. You've spared us from god only know how many more hours of blankly staring at our professors over complicated lecture slides. Thank you so much.

[jacktrooper]

Finally I am enjoying learning Fourier, I didn't have maths teacher from high school to whole engineering, learning by myself through a secondhand books without internet videos or colorful explanations was total madness...current students should feel lucky with such resources.

[willaldington]

Extremely clear and useful! Just wish I didn't have to pay 9k a year to get a worse education that I can get for free on youtube! Thanks a bunch

[sciencoking]

I spent 2 hours watching another lecture on this and it drove me crazy because it was all theory and I had no example to "play" with or hold on to - You taught me in 30 minutes what the other guy couldn't in two hours - Thank you :)

[zxmdb]

From the bottom of my heart, thank you

[TheCoinChannel]

I've gotta say, your videos are so well-explained that the material and the video content goes by so slow to me, yet they are so engaging that they end so quickly! You are a great instructor, and I really appreciate all of the awesome content you put out. I know you help out so many people (including me) and I really appreciate it.

[r.alhilal]

I study computer engineering in Germany and we are doing signal processing now, your videos saved me ! you don't know how grateful I am to you, I shared your videos to everyone in my class.

[BlueCliff]

This is phenomenally better than the $1, 000 stress-inducing class I'm taking right now. It's ridiculous how much easier this is for me as a slower learner, being able to pause and whatnot. It's much better than being lectured at for three hours a week just to have to go home and read the textbook in order to actually be able to grasp it.


And that's actually how every one of my classes goes. Thanks, college.

[gigajoules]

Thanks a lot, I'm an electronic engineering student so I have this coming up in exams soon. I'm a very visual learner so your teaching style helps me a lot.
Now I understand WHY this works and not just HOW.

[ahassan]

hey emmanuel, the easiest way is to look at the symmetry of the graph of the function. An even function would be symmetric with respect to y-axis (mirrored across it), and an odd function would be symmetric with respect to the origin.

[snakyeyes]

Thank you @Big Bang Physics
It was a good video to start fourier series again. I am studying Fourier after about 7 years now.
This video really helped. In fact, just so you know, I have recommended this video to my friends already :)
Please keep at it. Thanks again.

[ninjasownpirates]

We've been going over Fourier series for a week or two and I've had no idea what was even going on or what the purpose was of doing them. You cleared all of my questions up. Thanks so much.

[aurumon]

Thank you for this! Your videos on Fourier Series was the most helpful one for me out of the other videos I watched.

[Linase]

For those wondering how he got those values for sin(x), (2), (2/3), (2/5) etc...an easy way to check is to just put it on your calculator.
In my TI-89 I put...(integral)(sin(3x), x, -pi, 0) and I got the -(2/3) just replace my words for the actual symbol and your good.

[nabarun]

i love him! like he's gotta be the best teacher ever!😃

[RishavPandey]

For people with the sin(x) problem, see when we integrate its -cos(x) and integration period is from -pi to 0 and cos(-pi) = 1 and cos(0) = 1, So we get -2.

[davidravnsborg]

I'm a BSc Kinesiology student trying to learn this for applications in biomechanics and diabetes research. Your video is incredibly helpful, thank you!

[michaelomigie]

thanks man! you surpass these cambridge lecturers !