Computing Fourier Series | MIT 18.03SC Differential Equations, Fall 2011

[@nickflavor7307]

Everytime this guys turns his head back to the camera, I feel like he has something funny to tell me. Anyone else?? Great video MIT

[@langtonmwanza6689]

omg why did you mention it now i cant stop seeing it

[@jasonkwok2148]

Nick Flavor ,,,

[@nomipakistanli]

man i had to go back to see the video again and man.... u made me laugh and made my apartment up at night

[@benjahnz]

Very clear, nicely paced and good to see a blackboard instead of a white board

[@joshuaobanero684]

I prefare white Board.

[@turel528]

I believe that in our informational era knowledge should be shared to whoever wants to learn. And this video is an incredible high quality material. Thank you for educating people!❤️

[@kesinenisireesha7799]

U have given much clarity about fourier series how to solve problem.thank u sir.u'r way teaching style is awesome.

[@yuval260990]

Wow! it's amazing to see the high level of professor at High rank Universities . 5 min with you and it's so easy! Thanks

[@georgesadler7830]

Professor Shirokoff ,thank you for analyzing and computing Fourier Series. It is important to understand the basics of Fourier Series.

[@juniorcyans2988]

The best video of how to solve the Fourier problems! Thank you very much!

[@avectresormt]

The only Clear explaination i got so far

[@fayadhal-mosawi5175]

Thank you so much for doing an awesome job explaining all of this!

[@zephyrblooms]

Great video! By the way did anyone else notice how at 13:00 the dot he drew moved when he pointed his finger towards it? lol trippy shit

[@sageflorentino7513]

Thank you so much for making me understand this content… you made it easier to understand

[@peaceofmind6141]

All I could think about is " Good Will Hunting" lol. Excellent teacher tho

[@arianabedi]

Fantastic video! learned a lot, especially from all those "i should also mention" snippets that just clarified things beyond any text book generally does!

[@CatsBirds2010]

Well done and thanks for explaining in detail.

[@yasisalehi]

I miss having him as a professor at McGill. He was so amazing

[@oscarresendiz8615]

He is a T.A. ....

[@yasisalehi]

@@oscarresendiz8615 At McGill University he was a prof for MATH 270 for the Winter 2014 semester.

[@oscarresendiz8615]

@@yasisalehi ah i see thanks for clearing that up!

[@yasisalehi]

@@oscarresendiz8615 Np! :)

[@CaseyKlein]

Thank you!!!

[@laurynasstonys3235]

Thank you professor!

[@SS-pn7ss]

Great video thank you so much

[@RLDacademyGATEeceAndAdvanced]

Nice explanation

[@redgeladlad3670]

how is it -2/pi ??? when you solve for b of n? plsss help asap

[@gmail846]

Omg I finally understand it. It's better to do this stuff in real time since it's an infinite series. Just simply doing it from a work problem or getting out there with this without someone guiding you through these infinite series is not going to be beneficial.

[@THE_ONLY_GOD]

Thanks!

[@aneeshmamidi5614]

at 7:08, you mentioned that if an odd function which is 1 or -1 multiplies an even function it would be an odd function. isn't it the opposite? 1 x 2 = 2, 1 x 4 = 4

[@calvinjackson8110]

You are thinking of integers. Yes an odd integer times an even integer is indeed even as we see in 3 times 4 yielding 12. This is not true for FUNCTIONS. You have to recall some definitions for even and odd functions: F is EVEN if: F(-x) = F(x) for all x in domain of F. F is ODD if: F(-x)= -F(x) for all x in domain of F. From these definitions it can be proven that: If F is an even function and G is an odd function with common domain D, then the product function FG is ODD.

[@robertburbulea8503]

Relaxing voice, I'm going to sleep to this

[@Cuevashiguera]

Very good explained, thanks a lot :D

[@ricardo4fun922]

Very helpful as always ...

[@estebanlopez1701]

I like this guy

[@ballazoutengcindylaeticia1460]

How do you get -2/π

[@nuismai]

Did you find out?

[@tmb_1003]

​@@nuismai nop..need help

[@SergeyPopach]

what those coefficient integrals are coming from, dude? you need to explain what those coefficients are and why they equal to those integrands

[@samuelkamtande7579]

Good explanation bro

[@kitookelawrencee1490]

you superb teacher

[@ayahiaoui]

A good explanation thanks

[@mounikalakshmi5239]

very nice explanation sir tqq very much

[@95vinoth]

What is the amplitude of the final waveform? Is it -4/pi ? Why has he randomly chosen a point above the square wave?

[@mridulk81]

The amplitude is 4/π, the point he has chosen is an approximation because 4/π is slightly greater than 1.

[@Hsapien2point0]

How do you get from 1/π to -2/π?? Please give full explanation, thanks

[@vector8310]

Brings the coefficient -2 out from within the integration sign.

[@klaysoftware93]

Thank You verry much

[@oussamaelajjaj6137]

Tfoe gay

[@camilomuianga7865]

Beautifuly done, however i've got some question. How are we going to realise that f(x) is either an odd or even functions by the way?

[@googoogaga_]

If the graph of the function is symmetrical about the y axis (so mirrored across y axis), its even (so if f(t) = f(-t) then the function is even) , if the function is symmetrical about the origin (if flipping it across the x and then y axis transforms it to its original position) then its odd (so if f(t)=-f(-t) then function is odd). If neither condition is met then its neither even or odd

[@sergiohuaman6084]

omg he drew the vertical lines! does it mean he is an electrical engineer? :O (see Lec 16)

[@goranm492]

Why f(t) is odd ???

[@HeatherAndClodagh]

How do you know when it's continuous or piecewise?

[@michaeltsike5059]

Excellent explanation altogether though. :)

[@UNFORGIVEN1821]

What about the exponential form.

[@srilekhaas4468]

Is it write from the beginning of calculs

[@ada4590]

kinda looks like Walter White Junior from Breaking Bad.

[@Nino21370]

OMGGGG IT DOES and I can’t unsee it😂😂😂😂😂😂

[@aneeshmamidi5614]

at 11:43, how did you get the -fourier series equation? please elaborate?

[@Pavan_Gaonkar]

Just look for Fourier series equation at 3:33

[@Mountain-l9y]

Why is F(t) an odd fn?

[@michaeltsike5059]

Please why multiply by -2 instead of 2

[@julianarias5688]

Why does -1/n become 1?

[@Dantheon]

He factored the n outside.

[@greatestever6983]

so...... I'm going through this now and An is not f (x)cos nt it's fx cos ((npi x)/L) same for bn is fx sin ((npi x)/L) so please explain what I'm missing here

[@greatestever6983]

Yes. I am comparing it to the exact problem from a book from diff. Eq. Class and the way it is being done here is by the book but we were taught a different and easier approach imo

[@greatestever6983]

Agreed

[@timotejkochjar9225]

Thank you Walter Jr.

[@mdsarwar5273]

In 5:50...how can u integrate 1 and -1 without dt?

[@matiasvarrone7021]

Md Sarwar He forgot dt, no problem. It's comprensible

[@Abcdeee_p]

love u

[@hanifanmohamad2327]

yeay

[@pheonix_002]

👌

[@MrKorrazonCold]

Tap the side of a round bucket of water. . ..Because you left out the input resonance vector direction 4pi +1=0 now forming the total oscillating amplitude of Sine Wavefronts at each and every point of space compressing 3D Wave Centres of Energy +1=0 now -1 de-compressing Two Opposing Spiral Vortices.. . .Or Huygens 4pi Spherical Wavelets contracting +1=0 now -1 expanding Virtual Pair's Spiralling out of existence.. . .Tap the side of a round bucket of water. . ..Because the Virtual Pair's are formed by the probability Sine Wave function in Quantum Physics. . ...Thus the total amplitude of Sine Wavefronts, or the magnetic fields rather like pistons within a cosmic pond, are always at right angles to the forward momentum of the electric 2pi Spiral Current.. . . Thus at the positive surface of a negative expanding light sphere compressing the wave amplitude the photons inward absorption +1=0 now -1 outward emission between the two previous vectors forms 2pi Spiral Radians 360 degrees de-compressing expansion.. . .And not compressing energy contraction +1=0 now.. . .Time is inverse multiplying energy compression +1=0 now -1 dividing expansion like frequency and wavelength.. . .Tap the side of a round bucket of water. . ..Because the total amplitude formed by a rings of inward spherical sine waves coming into each and every point colliding at maximum compression points at wave crests and wave troughs always seeks a minimum +1=0 now are equally balanced by opposite expansion -1 at interchanging compression points . . ..As trillions of inward Spherical Sine Waves cancel +1=0 now the sum of opposite vectors mathematically is always zero. . ..(Zero Point Field).. . .Leaving space with an average temperature, or pressure stillness of the wave amplitude squared. . ..This polarized super position of the wave amplitude squared is the reason for entanglement, for the symmetry or conservation laws in human physics or why, at the speed of C, time and space are zero due to length contraction and time dilation. . ..Or why the point of charge Q remains the same for the entire surface of a negative expanding light sphere.. . .Because the photons input +1=0 now -1 output polarization in between the crests and troughs will remain the same (Sharing the same entangled moment of time) no matter how large the positive surface of the negative expanding light sphere becomes until acted upon by an external force.. . .Vibrating sinusoidal Spherical Wavefronts of Only Spiral Motion always transverse One unit of space Now per One unit of time dilation, or energy input +1=0 now.. . .Light is simply space divided by time entanglement and nothing else.. . .That implies a strict equivalence between time and space within light being the constant conversion unit between the two.. . .Tap the side of a round bucket of water. . ..Because everything is formed by a surrounding 4pi Spherical inward absorption +1=0 now -1 outward emission of electromagnetic waves.. . .Velocity = Time Density +1=0 now -1 Density of Space Time G/r2.. . .All motion is 2pi Spiral.. . .And all 3D directions are 4pi Spherically curved.. . .Thus Wave Centres of Photon Energy E=hf are everywhere relative to an infinite future of potential possibilities, shaped rather like onions relative only to their frequency f continuously coming into +1=0 now -1 out of existence, forming the total oscillating amplitude of Sine Wavefronts at each and every point of space Compressing 3D Wave Centres of Energy +1=0 now -1 de-compressing Two Opposing Spiral Vortices.. . .Or Huygens 4pi Spherical Wavelets contracting +1=0 now -1 expanding Virtual Pair's Spiralling out of existence.. . .Therefore from the continuous stimulated emissions as time unfolds C2 into the future visible light is just an added pressure condition to a wave medium that's already there continuously coming into +1=0 now -1 out of existence .. . .Like the zeros and ones of a computer screen with the Planck's constant h continuously forming a blank canvas that the observer can interact with turning the possible into the actual...

[@pcbworks]

me in the exam: ta ta ta

[@avalazem]

He looks like a white version of Chapo from narcos

[@KumarHemjeet]

ok

[@cagdasgul3322]

Plus ta ta ta...

[@tundedongo3373]

Uj

[@surajkeshari9991]

Thank you professor.

[@dauruei9919]

Nice explanation