Fourier Series: Finding a Fourier Series Representation of a Function

Fourier Series: Finding a Fourier Series Representation of a Function
In this video, I demonstrate how to find the Fourier Series representation of a simple piecewise function with a period of 2. The process is lengthy but essential to understand for anyone studying Fourier analysis and its applications. Although I do not provide a proof for the coefficients' formulas, I use the theoretical background from earlier videos (check out the playlist for more). By the end of this video, you'll be able to break down a function into its Fourier series components and gain insight into the representation of periodic functions.

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What You Will Learn:
How to find the Fourier coefficients for a piecewise function.
How to set up and evaluate the integrals for coefficients.
Understanding the sine and cosine series that make up a Fourier series.
Applying the formulas for a_n and b_n and a_0 to represent a function.

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[amanjotwani]

Test in 2 hours. 1) Open the channel. 2) Watch the video. 3) Done in 20 minutes. 4) Practice. 5) Ace the test. Thanks Patrick!

[Dantheon]

I've struggled with this for 6 months and you've made it clear in 20 minutes. I don't have words to thank you enough.

[Edalvaren]

I saw your video about the revenue cut and being a Patron. I then remembered this particular video. If it hadn't been for this video I don't know how Continuous and Discrete Signal Analysis test would have gone. So thank you Patrick for teaching me how to compute the Fourier Series Representation of a Function. I am heading over to Patreon Now as all of your math videos have helped me more in life than my $10 netflix account or my $10 spotify account. Good luck!

[AndrewEG]

what I find neater, is not the function, but the fact you have helped hundreds and thousands of people with maths. I reckon you'd feel pretty good about that Patrick.. Thanks for the video it's really appreciated! 

[sheilasmith]

Thank you so much, the step by step progression that you use makes everything so incredibly clear when previously it looked like a whole bunch of random equations thrown together with no continuity.

[DescartesRenegade]

This topic alone was the reason why I dropped my Quantum Mechanics class. This was never taught to me and for the life of me I could not understand it. The last 20 minutes was perhaps the best spent time in my life thus far. 

[boomsaway]

I love how this guys makes topic the easiest it can be unlike all these university lecturers who just assumes we already know everything.

[HuangDarren]

2L = period. (standard formula)
And since period = 2.
2L = 2.
and L =1.

[dianaingato]

My end of semester tomorrow... Im clutching on your tutorials.. Thanks big..

[AidenGerhart]

Missed a few days of class from being sick, so I was completely lost when I came back and everyone was talking about Fourier series and nothing else I looked at helped me understand it whatsoever

You're a total lifesaver, man

[braedensmall]

Seriously you basically taught me the entire Calc Series and Linear 1 and now this is saving me in Linear 2. THANK YOU. So blessed to have such a clear way of learning this material available to me through your videos. So helpful, you have no idea how many of my fellow engineering friends have used these videos to learn!

[liger]

Please do another harder one! Also thank you for your videos, I cannot describe how valuable of a resource they have been for my classes.

[inzamamulislam]

You are the best ! So much better than any faculty at my university !

[zeyad]

how's this bro, been saving me since 9th grade and now I'm about to be in my 4th year of engineering . Absolutley insane. Him and "organic chem tutor" are the absolute legends of the core science based classes.

[bradleykopp]

Thank you so much, Patrick! You are a life saver! I didn't understand Fourier Series at all until watching your video, now I think I can get them down in time for my final!

[TheCampbellbme]

Awesome video. Been using your material to help me for four years running. Bout to start graduate school for electrical engineering (undergrad is biomedical). It would be epic if you did a video on wavelets!

[safafituri]

Patrick you are the best !!!
you explain things smoothly and as if you are reading what's on our minds.
Thanks in a million.

[tonytoons]

have to say you saved my session. Good work! I wish my teacher would explain as good as you.

[ncandescence]

how do i unlearn the complicated way my teacher taught me? :-( :-(

[modernwarrior]

i dont even know who my math prof is or when the section hours are thanks to you. really convenient and time efficient videos. that was the last term with math for me but i suppose im still gonna linger here for a while.