Laplace Transform Explained and Visualized Intuitively

Laplace Transform explained and visualized with 3D animations, giving an intuitive understanding of the equations. My Patreon page is at / eugenek

[@EugeneKhutoryansky]

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

[@interstellarconveyance4865]

Hi Dr. E.K.! If we can measure the zeroth no time point, is their a way to multiply the Laplacian to show a function for the existence of an anti time equation in higher dimensionality? Mind blowing segment at 1:43&:44 seconds. Thank you.🙏🏻 I.C. MSc Astro-fizz

[@gayathrivijayan5591]

Mam need in tamil language

[@joaosol7234]

"[...] the Laplace transformation provide a method to EASILY solve differential equations [...]" Every day I'm called Dumb in a different way

[@TheConsuela101]

w/o initial conditions it makes them super easy, video didn't even break into all the electrical and mechanical uses it has. These videos provide excellent intuition.

[@julianbell9161]

Understanding the proof of something is way different than actually using it. The proof of a Laplace Transform is very abstract. Using the transform, however, is very easy. I am an electrical engineer and Laplace Transforms make solving circuits very simple.

[@JuanGuzmanSilva]

I know that feeling

[@tiborbogi7457]

Good one. 40 years ago I learned this, but not used it. So I am as Dumb as you are. ;-)

[@EvilSnakeMechatronic]

@ebulating Easy for average University students. It may not be easy, for example, for Elementary school students.

[@AUSTINwazhere]

Fantastic, I have no idea what I just saw.

[@mbenitez6722]

it really be like that sometimes

[@durga18991]

@@mashfiqrizvee2537 follow RUBEL BHATIA MATHEMATICSkzbin.info/door/_wDGFo02ck_egU6upx6AkQ

[@planetyam6044]

im pretty sure it's a recipe for some kind of strawberry pie.

[@ylaronedo8540]

Watch it once every month 😂

[@darkseid856]

@@siddharthpandya7763 calm down mature boy

[@blazejfiderek5229]

Not only love the fact that all stuff is well visualised but also that every important information is both speaken and written for people who learn faster with their ears and for those who learn faster with eyes. Great job

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@shnutzer]

I used the Laplace Transform as a tool in my college classes, not knowing what it was really about. Finally, I understand what it really means. Thank you!

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@davidhenningson4782]

Fantastic. It really helps put equations into perspective when you can visualize the graph form through time. Wish we had today's computing power back in the early 90s... mathematics would have been more entertaining and easier to visualize back then.

[@griper00]

Even though we have it i found this randomly on my own because our teacher just writes stuff on white board or shows some presentations with equations. nothing else. the subject is called cybernetics i was finally getting excited for some fun but got math 2 instead.

[@ishac5878]

Today, I have a Masters degree in science. Came here to thank this channel. It has taught me so much more about maths and physics than last 10 yrs of formal eduction and, also made numbers therauptic for me. Much much much LOVE. THis channel is literally a GEM of KZbin!!!💓💓💓

[@EugeneKhutoryansky]

Thanks for the compliments. I am glad my videos have been helpful and that you have enjoyed them. And congratulations on your Master's Degree.

[@EugeneKhutoryansky]

If you like this video, you can help more people find it in their KZbin search engine by clicking the like button, and writing a comment. Thanks.

[@greenbeans7573]

Physics Videos by Eugene Khutoryansky You should make a Reddit and Twitter account and put it in your description. Would definitely follow.

[@jaikumar848]

great video..thanks for this.... I really want you to make video on z- transform ... I am still struggling to understand this...and not able to find its practical application. .

[@gtxalpha9107]

pls do a video on eulers identy n equation

[@es_for1]

Comment

[@jonasmanuel]

What Software do you use?

[@damjantasevski5769]

This videos are pure gold, I don't know how people used to learn this without youtube and stuff like this.

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?v=6MXMDrs6ZmA&ref=share You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@Blue.star1]

sucks, change the explanation and remove the music

[@Stevobulfer]

Hey, what playlists do you use for your videos? I would love to use them for studying!

[@jamesharbaugh5732]

It's beautiful... It's just corrupted by flawed computations of the base ten number system... so close.

[@Stevobulfer]

@@jamesharbaugh5732 where

[@jamesharbaugh5732]

@@Stevobulfer it's inherent in computing as base ten needlessly creates irrational numbers with infinite decimals that must be rounded and denies division by zero to set a constant lower limit much like plank's constant. Out of all real numbers all are divisible by one as any number divided by one is an identity. Half of numbers are even or divisible by two, a third are divisible by three but this creates an infinite sequence with 1/3 because ten does not have a prime of three. 1/2 =.5 1/5 =.2, 1/4 = .25, 1/25 = .04... I try you can continue the mirroring effect of inverse exponental primes moving by decimal place. Pi is a perfect denominator as a circle has infinite slopes from n/0 to equality at n/n to n/0 and cycling through the four subplanes with infinite divisibility (like a pi chart, pun)... you just need to put absolute values on the Pythagorean theorem to better define i and render locality for more polarized locations. I could ramble on and I know you won't listen or care... It's nothing the video creator did... It's just built into the system. Base 60 was better but not perfect, a notional pi fraction would be and could bind infinity as well as introduce some cool number logic.

[@RedVenomProductions]

Mathematicians in the past could only dream when they see this.

[@ShahedVideo]

i just wonder how anyone came up with all this in the first place

[@kothekarswaraj]

those computers in hands of old mathematicians are no different than infinity stones with thanos

[@howmathematicianscreatemat9226]

I agree. Only true badass mathematicians like Gauss and Euler would have been able to imagine this in their brains. It faaaaaaaaaaaaaar exceeds normal imagination skills. It’s like the difference between the distance earth to Moon versus earth to ☀️

[@howmathematicianscreatemat9226]

@@ShahedVideo for such beautiful math someone needs poet mind and super awesome spatial imagination skills (for the inventing of such). But with lots and lots of experiments I’m sure you would find some important new concepts too, not just people like Euler or Gauss.

[@kevinbyrne4538]

Just in case anyone is curious, the music is: Liszt's Hungarian Rhapsody No. 2

[@D3tyHuff]

Thank you!

[@mathiasfantoni2458]

THANK YOU!

[@miholju]

I wasn't sure what that was, lol.

[@Bilangumus]

Haha, I was looking for it, thanks

[@gaurangagarwal3243]

I heard that once in an episode of tom and Jerry lol

[@nothinginteresting1662]

One thing Eugene taught me is that sine wave is not that 2d wave which we are taught, but actually circular motion moving with time. So powerful and elegant concept to know! Thank you so much☺

[@EugeneKhutoryansky]

Thanks.

[@AlphaCrucis]

Careful. The spiral you are seeing is actually two sinusoidal waves being added together according to Euler's Identity: e^(iwt) = cos(wt) + i sin(wt) In order to get a flat sine wave from those complex exponential spirals, you need to add a positive and negative version so they rotate in opposite directions like this: 2 cos(wt) = e^(iwt) + e^(-iwt)

[@nothinginteresting1662]

@@AlphaCrucis The 2d sine wave is a projection of this spiral. Even Euler's formula gives a point on a unit circle in complex plane. e^(iwt) is actually a point on a unit circle that changes w.r.t. time. Now if you think that this point not only rotates but also moves out (or goes into) the plane of rotation with increasing time, you get this 3d spiral. When you add the conjugate of e^(iwt) to itself, only the real component of the complex point remains; the sum is twice the real component of e^(iwt). So it appears that only x coordinate is changing and there is no rotation. But there is rotation, just that it is confined to one dimension. So my point was that the sine wave we are taught is what we see when this spiral is plotted on a flat 2D surface like screen or paper. Maybe we can confirm it with holography. In fact, I believe in higher dimensions like quaternions, this would relate with direction cosines. In two dimensions, sine and cosine are direction cosines of a point.

[@hammer9749]

Thanks for your time invested furthering our understanding and knowledge, Eugene Khutoryansky. Appreciate Kira Vincent's excellent and engaging speaking voice.

[@EugeneKhutoryansky]

Thanks for the compliments.

[@douglasfreeman4526]

Манфрэд Hammer qq

[@lordmurphy4344]

Damn, this almost brings a tear to my eyes. Definitely a sight to behold.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@sciencecompliance235]

You sure it's not the Liszt piece you're reacting to? This one has had that effect on me before.

[@miholju]

@@sciencecompliance235 I try my best. Hope you like my music

[@kilrmonjaro]

3rd year student of physics here, Thank you. Sincerely. You have brought years of practice together into an harmonious intuition.

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@mangeshmalgi279]

This is a great animation. It's for the first time, I found such a lucid explanation of Laplace Transform.

[@windyo5535]

If you haven't seen them yet, I highly recommend his videos on the wave function and Fourier transform.

[@mr1enrollment]

Hi Eugene, I am a retired EE, it has been 40+ years since I studied Laplace transforms. I enjoyed the video and yet it is still mysterious as well as wonderful. I would enjoy seeing applications like multipole LRC circuts solved in this manner, as well as the duals in mechanical Mass/Spring/Damper systems. For extra credit - adding an amplifier to make a notch filter would be interesting. ---Also what programming language did you use to create the video and is the code open source? Dan

[@thefreemonk6938]

You have subscribed to some damn good channels.

[@mr1enrollment]

@@thefreemonk6938 Nice of you to say so.

[@sclabhailordofnoplot2430]

@@thefreemonk6938 The founder of youtube smiles upon you.

[@smishpattu3323]

I have subscribed to your channel and I truly believe that this is going to become one of the best channels ever. Ever. Just keeping work on your videos and you never know where you will be in a few years. Cheers! Btw, what do you do? Are you a teacher?

[@EugeneKhutoryansky]

Smish, I am glad to have you as a subscriber and thanks for the compliment. As for the question about my background, if you type my name into Google, you will find a lot of information about me. :)

[@mohammadhaseeb7392]

@@EugeneKhutoryansky I just saw your profile on Google. Amazing

[@mohammadhaseeb7392]

@@EugeneKhutoryansky By the way, I'm a Chemistry MSc . Just subscribed. Eye candys by the way

[@AbdulelahAlJeffery]

I really wish if more videos like this were made for the more basic and fundamental concepts in mathematics. This will bring more viewers and help those who already know the basics to understand it even better with the 3D animations.

[@EugeneKhutoryansky]

I also have videos on basic topics, in addition to videos on topics like this one.

[@TieXiongJi]

Math is awesome. Good job La Place! Got me through electrical engineering without being a math whiz.

[@the_kingslayer]

Laplace had a level of genius right up there with Gauss, Maxwell and Richard Feynman!

[@anadawaween]

nobody is as genius as gauss.. all the other people you mentioned combined are far inferior to gauss' genius

[@ahmadbelial9778]

True but you didn't mention euler and that's understandable because he is from another dimension

[@numv2]

Lagrange is the real beast

[@Srinivassss1999]

Y'all know your geniuses alright xD

[@seandafny]

Srinivas Prabhu lhh

[@msyturk_]

I have always thought about similarity between laplace transform and fourier transform. This video is so descriptive. Thanks a lot

[@Kobs.A]

Fourier is a subsection of Laplace

[@malmalhi007]

those of us undertaking electrical engineering in the last century would have benefitted vastly if these visualisations existed then

[@Compguy321]

8:35 Computer says: forget it, this is too complex, not calculating the dots anymore 😂

[@tichbyte9352]

Lolz

[@shayanmoosavi9139]

COMPLEX you say?! :)))

[@kevconn441]

Love your videos. This one way over my head, but I have learned a lot from the simpler ones. Thanks.

[@kummer45]

This is exactly a clean explanation of the Laplace transform. The video doesn't simplify it it to make it user friendly. This video describes it in all the details. This is a video that must be in every classroom because it doesn't dodge the problem by intuitive explanations. Math is exactly this, complexity and the analysis of behavior. This is an outstanding video that fully describes what is going on.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@MrSinusu]

Amazing to see how easily this video explained the subject. Of course, I haven't understood a bit.

[@joy2000cyber]

This is better than undergraduate engineering class of MIT and Stanford together

[@EugeneKhutoryansky]

Thanks.

[@klam77]

the MUSIC is poorly chosen, Bach's sonata would have been SO much better. In fact the music completely destroys the understanding. How could he have been so callous! How could he not have paid attention to the music. It's so wrong. (LOL).

[@Roulises]

I did not know that a class at MIT was so deficient.

[@blueyetimicrophone3301]

Nice humble brag

[@sarielreigns777]

USAss is so crap

[@jugnoopks]

Dear Eugene Your channel and your videos get the maximum number of responses in shortest time. It's my third comment that too before 24 hours of it's posting. But you know I am dumbfounded. Lost my words for the appreciation of your videos. What ever they are. These videos will be greatly appreciated by future engineering students. And as I always say keep seeing physics. Sincere regards.

[@EugeneKhutoryansky]

Thanks.

[@thetedmang]

Arguably the most important math/physics channel on KZbin. Thank you so much Eugene.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@hardikpande6970]

An etheral voice expounding how purely mathematical constructs, scintillations of the human mind, harmoniously describe the course of nature. In one word, beautiful.

[@EugeneKhutoryansky]

Thanks.

[@senthilkumaranmahadevan6531]

Dear Eugene Khutoryansky , your videos are brilliant .... its a real contribution to Maths & physics ......Keep going..... I use your methods to teach in my class rooms people like them..... you have inspired many people through your brilliant imagination and knowledge..... thank again for explaining Laplace in your own style.... Hats OFF

[@EugeneKhutoryansky]

Thanks for the compliment and I am glad that you like my videos.

[@darrennixon8765]

I am grateful for your existence.

[@EugeneKhutoryansky]

Thanks. :)

[@eriksundell1400]

Writing that comment for KZbins algorithsm! The work you do is awesome! Thank you!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@swampwiz]

The Laplace transform was a great example of something in my Mechanical Engineering coursework that I had mechanically mastered, but didn't really grok it for what it means. These videos are opening my eyes.

[@EugeneKhutoryansky]

I am glad my videos are helping you see it from a new perspective.

[@voimr8659]

Amazing, I'm really excited after watching the visualization. The Laplace transform is useful for analyzing continuous function, yet it can not be used for discrete signals which need z-transform to analyze. Can you make the 3D video for explaining z-transform? Thanks a lot.

[@DavidMorley123]

Excellent. Beautiful graphics. I hadn't thought about this stuff for decades. It brought it back to me in the most beautiful way.

[@jamescarmody4713]

I love everything about these videos. The subject, the visuals, the captions, the music--it's perfect!

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@miholju]

Music... perfect... as I expected it to be.

[@darkswordsmith]

A picture is worth a thousand words. A video is worth years of studying and thinking. Awesome!

[@EugeneKhutoryansky]

Thanks.

[@nicolasjulemont]

Wow men ! This is just crazy. I can not imagine how much time you have taken to make this incredible video. Honestly, it is amazing. I am just very curious to see what is going next, when you will want to explain transfer function and laplace transform together.

[@benyseus6325]

Every electrical engineer is familiar with these concepts, sadly 😢

[@leonkayombo4316]

Nothing interesting except the classic music

[@user-ju8qg9dx9x]

First time I saw this video when I was in K-12, I had no idea what you were talking about. But this is the second time I watch it as a 2nd year engineering student, your video has been of great help.

[@seamus9305]

Elegance, beauty and knowledge. Some think the universe is made of triangles, but I think the material universe is made of spirals in time. (not that I understand the math)

[@TonyRios]

This should be added to the differential equations class

[@windyo5535]

You hit the nail on the head. It's impressive how well he can distill these concepts down to something simple and intuitive. Adding the depth and detail is a breeze after that.

[@TheArnoldification]

"bruh don't even worry about this diff eq shit lmao just use algebra" ~Laplace

[@TheTurtleOfGods]

"YES YES YES" ~Laplace

[@user-up3yq6pt3v]

Это просто потрясающе! Подобные визуализации должны стать частью образовательной программы!

[@AzEsm777]

да, согласен. Когда то, безуспешно изучая верхнюю мать- еë-матику, я игрался в Maple V рисуя графики простейших алгебраических и тригонометрических функций. Не скажу что в школе учили плохо, у нас была замечательная, влюблённая в предмет математики преподавательница. Но, только появление персонального компьютера и дисплея в моей жизни смогли визуально растолковать закономерности и зависимости в формулах. Я начал "чувствовать" поведение функций типа cos 2x или e^sin(x^2). Успехов не достиг, но уважением к предмету проникся. 8)

[@ExternusArmy]

this is seriously the best and most underrated physics channel on the planet. i tell all my classmates about this channel

[@ExternusArmy]

sometimes i wish your videos were out sooner so i could reference them in time

[@EugeneKhutoryansky]

Thanks for the compliments and thanks for telling your classmates about my channel.

[@VinhBui-qo8iw]

One of the best explaination of the Laplace transform. Thank you!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@vaishnaviborgaonkar5217]

I am impressed by your way of teaching , it's amazing 👍

[@EugeneKhutoryansky]

Thanks for the compliment.

[@olbluelips]

This is really beautiful, thanks! I appreciate the deep understanding necessary to create 3D visualizations

[@EugeneKhutoryansky]

Thanks.

[@dp0813]

As an electrical engineer working with RF & signal processing for 4 years, this is GREAT stuff! Gives more intuitive meaning to these difficult mathematical concepts. I just could do without the loud classical music lol

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@josealonso8431]

I would really have a hard time trying to analyze and imagine this in my head. Thank you so much

[@EugeneKhutoryansky]

Thanks.

[@alfonshomac]

really cool video as usual Eugene.

[@EugeneKhutoryansky]

Glad you liked it. Thanks.

[@Saxshoe]

Thank God, just in time for Process Controls and transport functions

[@justinstark5732]

2nd year physics student here, only used them for solving ordinary differential equations so far. Never seen them visually represented before

[@ylaronedo8540]

Eugene you are the reason i am going to study control systems and also the reason i passed my Mechatronics with cum laude can't thank you enough

[@EugeneKhutoryansky]

Thanks. I am glad to hear that my videos have made a difference.

[@EDUARDO12348]

This is amazing and motivational to continue learning math. Thank you for awesome work!

[@joanmasde3535]

What a beatiful transformation omg i'm amazed

[@EugeneKhutoryansky]

Thanks.

[@anilkumarsharma8901]

Jaisey karni vaisey bharni Jaisa boyega vaisa karega As you sow so you reap All the universe following a same function in every possible respect

[@elonyao3894]

To be honest, knowing the calculation method first,then using this video to get a deep understanding is a better way

[@andresbrocco]

You are awesome! Could you continue this video series with a video on transfer functions? O would appreciate It a lot

[@EugeneKhutoryansky]

Thanks. A transfer function is just the Laplace Transform of the unit impulse response.

[@stephanosphilippou1300]

Nice visual effects . But please take the time to explain what you're talking about, otherwise its just as another comment says: colours with music

[@miholju]

Good music

[@CristianDiPuorto_glockshock]

What can I say... I already knew about the Laplace transform but now I really feel it in my bones. Thank you Eugene.

[@EugeneKhutoryansky]

Glad you liked my video.

[@Taka-tb4ki]

I’m not a native English speaker.But it’s close to clearly get that. It’s so helpful.

[@MrNukenin16]

How do you do animate such amazing videos? What programs do you use or do you do it programmatically? Again, excellent video, as always.

[@windyo5535]

Comics Entertainment Studio He uses Poser.

[@EugeneKhutoryansky]

Thanks for the compliment. Yes, as Chira said, I make my 3D animations with "Poser."

[@jaikumar848]

really want you to make video on z- transform ... I am still struggling to understand this...and not able to find its practical application. .

[@mr1jon1smith]

jaikumar848 it's used in electronics in sampling signals...

[@jaikumar848]

mr1jon1smith I know. ..but could you please elaborate?

[@harringtonindustrys]

Bruh Just Think About it...

[@seandafny]

Its the same thing. Just discrete

[@patvdp6754]

I never would imagine one day understand the Laplace Transform with a circus music. Thank you Eugene for your work.

[@naifalotibe3862]

The best explanation for Laplace transformation I have ever seen...well done.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@saidutt5167]

just awesome.....your animations are too good

[@EugeneKhutoryansky]

Thanks.

[@Redant1Redant]

I couldn’t follow this. Something is missing. Like what is being transformed to what.

[@mr.champion7304]

there are 2 functions here, A function which takes some time value(I'll call this f(t)), and outputs a value for some input of time. Then there is its "Laplace transform", which shows the "frequency" of f(t), given some complex number s(I'll call this function F(s)). However, there are 2 different transforms this video goes over, the first transform the video explains is the transformation from F(s) to f(t), the second one is from f(t) to F(s).

[@DarthZackTheFirstI]

somehow the video doesnt actually show how the calculation is transformed. thats what i actually miss in those videos. without previous fourier and some math books i wouldnt know what she tries to show. with a real equation going over all the animations would be more interesting. so its only showing the two parts.

[@tissuepaper9962]

@@DarthZackTheFirstI the video literally showed both of the integrals you need and explained every term.

[@my-crazy-fantastic-fanatic]

7:42 - *gets lost in how beautiful the lines are and has to start the video all over again*

[@federicopaulin]

I have my final exam about this topic on Friday. Many thanks, this video helps me a lot

[@EugeneKhutoryansky]

Glad my video came out just in time for you.

[@seandafny]

Eugene i remember when i was like the only 1 watching your videos. Im so proud.

[@brianlamptey4823]

0:01Uhhh, so what is the Laplace transform?

[@Roulises]

I always wondered, what the hell is it for me to learn this? I studied food engineer degree I didn't know where I could apply this. I finally see and understand what works. Incredible as I can now give me an idea of how fascinating mathematics is with this vídeo. Greetings from México.

[@jacobrick6515]

Currently taking Process Dynamics and Controls where we use Laplace transforms on the daily..This video has given me some spine bone chills!

[@sorh]

thanks mate, now I'm even more confused.

[@yassinebouchoucha]

is that all about Laplace Transform ? I still didn't get it , when the part 2 be released ?

[@user-km2tp5lo7e]

I keep coming back to watch the cinematic, so intriguing.

[@TheChrasse]

Very nice video! I have already taken a course on Fourier transforms, but not yet on Laplace transforms, so I did in fact learn something useful from this video. Keep up the excellent work, Eugene.

[@EugeneKhutoryansky]

Thanks.

[@yaribsuarez8725]

Hungarian Rhapsody yeah!

[@miholju]

But of course.

[@ahmadbelial9778]

Unmm I have a question, WTF

[@seandafny]

Lmaooooo

[@leecoates]

I'm studying Laplace transforms for MechE degree and I was blindly reading through a hefty tome applying a rote learning technique, I am somewhat lost as I didn't have a scooby doo what the eff I was looking at. Then I watched this video and I must say it's like I've just put on a new pair of glasses for the first time! What beauty! A fantastically well put together video! Thank you.

[@EugeneKhutoryansky]

Thanks for the compliments. I am glad my video was helpful.

[@VincentDavis1]

This is an excellent video for viewers that do not have a rigorous scientific background.

[@kostop4569]

tom and jerry the cat concerto 1947 thats why the music sounds so familiar

[@miholju]

You're welcome

[@ExemplaryLigas]

Thanks a lot, is so abstract even with the graphic representation, regards

[@vector8310]

So much symbolic abstraction made beautiful and crystal clear!

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@Vk-gv3sc]

thank you eugene...for your videos..i am so happy while watching it...when my prof said...i could'nt understand at all......and your animation quality has also increased.

[@schrodingerscat3486]

Beautiful

[@EugeneKhutoryansky]

Thanks.

[@_yuri]

Nice music dude

[@wenhanjiang464]

pink Fungi liszt's hungarian rhapsody no.2

[@miholju]

I'm glad that you enjoyed it.

[@the_kingslayer]

Another amazing video thank you! I just took control systems and math physics for my electrical engineering degree last semester and had a very hard time conceptualizing the different system responses, makes way more sense now!

[@EugeneKhutoryansky]

Thanks.

[@emilyzhang5651]

Wow. Haven't learnt what Laplace transform is but now that I've seen this, I think I got an idea! Great job! Love the cheery music going on in the background haha

[@a.m.1298]

Awesome!!

[@EugeneKhutoryansky]

Thanks.

[@XpressCrosSs]

thanks you a lot !

[@EugeneKhutoryansky]

You are welcome and thanks.

[@XpressCrosSs]

you deserve more than other garbage youtube channels, we are supporting you. just keep going ...

[@IQ88612]

you are doing soooo great not just well , the creation of videos ,the knowledge needed for those videos , I've watched some and you are astonishing me every time, good luck

[@davidlanderos3963]

[cries in differential equations]

[@Jarrod_C]

did not understand this at all. I have taken differential equations and other engineering classes, i.e. signals, but this is not intuitive.

[@obinator9065]

Well I didn't took any of those and still understood it. Maybe some lose at complex numbers...?

[@Pulsar77]

Someone's been watching 3Blue1Brown...

[@duckymomo7935]

Pulsar77 that’s the Fourier transform

[@Pulsar77]

I know that, and I'm sure his video inspired this one.

[@EugeneKhutoryansky]

Pulsar, that is not the case. I did a video on Fourier Transforms in 2015, and I had started on the animations for this video on Laplace Transforms long before 3Blue1Browm released his video on the Fourier Transform.

[@NeilGirdhar]

It's not a problem if you cover some of the same material as he does. Both yours and his channel are outstanding.

[@romanemul1]

This guy has been here long before 3B1B. 3B has been inspired. Somebody is watching too much 3b

[@bradleyrwerner]

Brilliantly simplified, elegantly illustrated! Superb, as always!

[@EugeneKhutoryansky]

Thanks for the compliments.

[@motaaaa]

This is very enlightening, now it got me wondering if we could create a transform even more general than Laplace, where not only the amplitude of the sines can vary but also their frequency, like the summation of infinitely many frequency modulated signals, but that sounds a little crazy