Real teacher teaches hardest concept in easiest simplest way possible and. I found you are the one who does beautifully Thankyou sir for giving such insight which we never thought possible without you "Love and huge respect from INDIA "
For those wondering why we need cosine as well as sine, one way of seeing this is to first observe that any function f(x) can be written as a sum of an even function and an odd function: f(x) = even(x) + odd(x) where even(x) = 1/2 (f(x) + f(-x)) odd(x) = 1/2 (f(x) - f(-x)) Now the sin(nx) terms approximate the odd part (as sin(nx) is always odd, a sum of them will be odd) and the cos(nx) terms approximate the even part (as a sum of even functions is even) the all we need is a constant offset as the average value of sin(x) or cos(x) over [0,2pi] is zero.
This is becoming my favourite math channel to extend the current knowledge with subjects that interest me. And youtube algorithm deserves a hats off as well. It just suggested your fourier series video series where finally it's not just introduction of what fourier does, but explaining how to use it or approach it. Like giving instructions to how to use a hammer to actually nail something.
Thanks to this video, I was able to explain a problem with a machine filling bottles. The machine was capable of filling 4 bottles at the same time. If a bottle would not be present the machine would not filled the bottle. But the weight in the bottles after that would vary too much and cause deivaitions. I was able to save the company about 1.2 Million per year. The product is very expensive.
You are the absolute GOAT of youtube teachers. I learn so much from you. You are getting me through DiffEQ right now. Best place to review for a test ever!!!!
Man, I have a final test on this topic on Friday. Pretty doubtful you would upload all vids related to this topic by then. Still, an amazing video tho! I’m motivated to learn now :D
i cant thank you enough Dr Trefor but your enthusiasm towards this topic helped me really focus on some underlying concept on fourier ,you really enlightened my mood this evening,thank you Sir
I know I'm going to sound like a complete d..., and I understand all that _"if you don't have anything nice to say, don't say anything at all"_ stuff, but... I'm going to take the risk of sounding like a total d... anyway, and present a bit of criticism about your style of presentation. I appreciate your enthusiasm, but maybe tone it down just a tad bit. You don't have to be a complete stick in the mud, but just a tad bit. It's genuinely distracting. It draws attention away from what you are saying.
Wow great video, I didn't saw this perspective of the Fourier series before. This is one of the subjects in mathematics that I like the most because at the beginning(when I was in college) it was difficult to me to understand it but once I discover what it does and how it's related to the Fourier transform it just blew my mind. Thanks for such awesome explanation videos!
The Dirac delta function(t) is 1 in fourier domain. That means that we need all sine waves of equal amplitude. cos(x*1/5)+cos(x*2/5)+cos(x*3/5)+cos(x*4/5)+cos(x) looks like an approximation to the dirac delta function, and it makes sense. Mathematically I don't understand why it's cos instead of sin, graphically I understand why. If we integrate by dividing with iw we get 1/(iw), which in time domain is a heaviside step function. That makes sense. 1/(iw) means that we want all sine waves, phase shifted by 90 degrees and their amplitudes decay on the form 1/(frequency). sin(x*1/5)*1/5+sin(x*2/5)*2/5+sin(x*3/5)*3/5+sin(x*4/5)*4/5+sin(x) doesn't look like a heaviside step function at all. Where am I thinking wrong? My gut feeling tells me that the heaviside step function is basically just a square wave of infinite period, shifted up and scaled down so it goes between 0 and 1. Sorry for coming here with such a mathematical question. But I thought it was very related to the video.
sin is an odd function (sin(-x) = -sin(x)) while cos is even (cos(-x) - cos(x)). The Dirac delta function is even (it is the limit of even functions) therefore needs to be approximated by sum of even functions.
gentle hint: your video would be vastly improved if: 1) you spoke more slowly and not in a continuous stream; and 2) you did not fill half the screen with a picture of yourself flapping your hands
if :(x max, y max)=(c/T , k*T^5) ,Where c & k. are constants Why : y/T^5 must equal f(x*T) ? I found this in some proofs in physics , what's the mathematical rule that be used here ?
I really dig how you end the video with questions to be answered later (but which a student could start thinking about ahead of the next lecture). I am learning how to teach mathematics effectively and your videos are incredibly helpful and inspiring. Thank you for the wonderful resource and I hope you don’t mind the compliments!
Great video. When I was first trying to understand this, my math prof told me, "The idea is any periodic function can be built up from sums of cos and sin. And... with a sufficiently warped mind, ANYTHING can be considered a periodic function." Even the Big Bang!! (hehehe... we don't know the 'period' yet, but one might consider it 'periodic') :)
Can I ask if for example a function f(x) = is a square wave having a period limit at -pi~pi/2, then suddenly converges to 0 at 0~pi, how do you approach the function? I am still confused about the discontinuity on your lecture. Thank you.
I came to your playlists for the topic I didn't understand from books or any source available on the internet. And I got my concepts here!! Some serious Quality work sir!! ❤️
When I see how well some random profs online can teach the broad strokes of Fourier Series, it makes absolutely no sense why other profs who, I'd assume are equally knowledgeable with regards to the basics, can't do a better job teaching the material.
Will you please make a long lecture serious regarding integral equations and then another series on integro differentail equations. Please also tell us why we use integral equations.
close, but you pulled the smaller periods (higher frequencies) out of a magic hat, if instead you potted (square wave *minus* sin wave) you would have seen something with a particular smaller period, etc, etc, etc, and no pulling numbers out to a magic hat
I always think is there any short of math application on romanticism. So many genius high minds are involved from the beginning of humanity in Mathematics. I don't believe that there is no Math application particularly developed on romanticism. Please give a video if you find some.
@Dr. Bazett - Great work. Enjoying your videos. Can I request Laplace Transforms, please? Perhaps this once I could figure out where it all came from. Only you can do this.
It may be worth noting that there's no mention of time in this explanation in the form of frequency . He says the period is 2*pi. When X gets replaced with w*t is when time enters the picture and the time domain is entered.
Awesome channel, thank you. Gibbs phenomenon is to be expected, though. One is trying to approximate a non-continous function by an infinitely differentiable function. If one was trying to draw this with a pen, it would necessarily overshoot due to its inertia (like in d²y/dt² here)
It’s a pleasure to hear you! Amazing content. Love from Portugal, I’m a physics teacher. Can anyone please help with a question: how to pronounce ao: a not or a nod?
I am so happy to watch this video - I understood concept of Fourier series with the happiest teacher I even seen. Much better understanding that in my university Thank you a lot❤
