What does the Laplace Transform really tell us? A visual explanation (plus applications)

[@williamstanley7775]

I am a retired engineering professor and taught this material for years. Yet I still find it very useful to see it presented by someone else since there is always some new perspective that I acquire. Excellent presentation!

[@joy2000cyber]

How did you become a professor in this area if you didn’t imagine this visualization in your head? By just memorizing the formulas?

[@williamstanley7775]

@@joy2000cyber Thank you for your question. I am now 82 years of age and we didn't have the visualization tools available today way back when I was in college. As an undergraduate I probably memorized the formulas and learned to use them to solve differential equations. When I was in graduate school we had to "dig deeper" and actually derive many of the formulas and procedures. Since my teaching was in engineering, we had procedures that vary slightly from those of mathematicians. I have taught much of the concepts using different approaches for much of my career and have written a couple of books based on electrical circuit analysis using transforms. Yet it is always helpful to see someone else develop a procedure because we can always learn something from another person's point of view. My best wishes to you!

[@joy2000cyber]

William Stanley Good for you having other approaches in understanding the topic. I was a student in feedback control and didn’t really understand FT and LT, which might be the reason I became a programmer. What portion of your students do you think had a good grasp of the topic by the end of the semester?

[@williamstanley7775]

@@joy2000cyber I suspect that only a small percentage really understood it on the first exposure and I suspect many never really understood it. To be honest, when I was first exposed to some of the more analytical subjects as a student, I obtained only a superficial understanding. Indeed even at my advanced age, there are still lots of topics that I don't understand! For example, electromagnetic theory has always been an area that has challenged me! Maybe in my next life (??) I will try to master that area. Thank you for asking and my best to you!

[@joy2000cyber]

William Stanley I suspect most my classmates didn’t understand FT, LT, control theory too. I thought we didn’t have enough practice with the symbols of jw, s, etc. Now I think we just need the visualizations and am a little upset that my teacher didn’t show it. Thank you for relieving me of the guilty thought of not being smart enough.

[@standard12th66]

When you procrastinate so much that you watch a video about what you are procrastinating

[@roystokes8435]

Lol so true xd, i should get my ass out of bed

[@momobobo74]

I feel personally attacked

[@aarongabraham6179]

Yep that’s me. I should be actually studying this topic for a test

[@JohnnyBladeakos]

thats me high af right now

[@justinw8370]

Yah sometimes when I’m lazy I’ll watch some KZbin videos related to what I need to study while I’m bed hoping that I make myself feel better. It’s not nothing, but definitely far less productive than working problems out and attentively listening to what is being said.

[@FireFox2382]

I'm seriously amazed that people from the 1700s figured this out while i could only understand it fully after seeing the 3D plots...

[@ashutoshmakwana3326]

Imagination

[@ayushkumar1539]

Seriously those guys were awesome., Then think about Einstein who give theories which work at speed of 💡🔦...

[@alex_linhares]

THEY DIDNT HAVE PORN

[@atomiccompiler9495]

@@alex_linhares Ah yes they had to imagine all the sex scenes since they were teens which improved their imagination power.

[@GizmoMaltese]

Imagine people like me who grew up without KZbin and had to try to understand this stuff from textbooks and teachers drawing diagrams on a blackboard. I'm convinced my teachers didn't understand the intuition and only knew the formulas. KZbin is the greatest thing to happen to education in human history.

[@TheDeviceReviewer]

This was brutal. I've been sitting in Differential equation/signals and systems classes in university and just performed laplace trafos without ever having a clue about it. Thanks

[@moressafrancesco]

Mee too man

[@abdulazizalhaidari7665]

Most of classical education student did the same, It is not just you .

[@vishnuskandata2355]

@@certyfikowanyprzewracaczhu3390 True...but ouchh. What did engineers ever do to you man??

[@cryora]

I always thought that s was real not complex. But that didn't really matter since the end goal was to determine Y(s) and then take the inverse. Differential Equations (1 semester) class was already packed with so many topics that you don't have the time to stop and analyze the form of Y(s) and what it meant.

[@williammische2409]

I have been an engineer for 12 years. I fully understood and loved the fourier transform but NEVER understood Laplace untill this moment. This was truly beautiful and comforting to watch. Thank you!

[@tenpotkan7051]

And I thought me not understanding it as a sophomore after a 90 minute lecture was bad...

[@k.c.sunshine1934]

As a retired engineer, I find the use of visual tools and youtube really enhances the intuitive understanding of this topic! E.E. Professors beware!

[@carnivalwrestler]

Universities and your dilettante-creating accreditation boards beware, you'll soon be peripheralized.

[@NazriB]

Lies again? Lap dance

[@Raghavendrabsrg]

​@@carnivalwrestler so its the same situation everywhere! Same here in India.

[@cryora]

What KZbin can't offer are credentials that employers will accept on a resume. Maybe if your employer is young he can relate with it if it comes up in an interview, but that is probably the only case, at least in the foreseeable future.

[@anjishnu8643]

Probably the most productive 20 minutes of my engineering life

[@anders5611]

Bad engineering life you've got

[@quantum7401]

@@anders5611 LOL

[@AlexJoneses]

Honestly same. Did what an entire semester long course couldn't do

[@cryora]

​@@AlexJoneses Even though it was a semester long, to me, it felt like a rush. That's because it was packed with so many topics, that you would not be able to cover any topic this deeply.

[@apoorvaamargol5125]

I've never watched a 20 mins MATH video at one go, trust me this is GOD LEVEL ! THANK YOU !

[@jamesbra4410]

You're to engineering what 3Blue1Brown is to linear algebra. Keep up the great work. Hey why don't you do some electromagnetics problems, those are fun.

[@L0j1k]

Hay check out Applied Science.

[@Guztav1337]

To be fair, 3Blue1Brown has a lot more than just linear algebra. He has different playlists if you check his channel

[@rotatoe]

You have an interesting definition of fun haha

[@AlexSKelly-up7lf]

@@rotatoe Lmao dont we all?

[@MrArianM]

You deserve a prize for this. It helps to "feel" what i have been doing just blindly for years in my engineering studies. Just perfect. Thank you.

[@aritrakundu1464]

I just finished my 3rd semester studying Electronics in IIT Kharagpur(the best college in India to get a degree in this field)....We were taught about Laplace and Fourrier transformations, pole zero diagrams, Transfer function, feedback, time shift, frequency shift, convolutions....yet I did not have this mathematical intuition behind Laplace transform...Zach please keep on doing this good work

[@shivamsharmaiitkgp8370]

100% truth.

[@nbarshain]

This is one of the most enlightening videos on KZbin. I have a hard time understanding things if I don't have an intuition about them, and this makes the concept super clear to me. This video should be required material for anyone learning this subject in school!

[@btCharlie_]

Due to my poor time management and the amount of material to study, I ended up blindly memorizing most of the stuff from control theory class, which comes to bite me every now and then. This is brilliant and much appreciated. Thanks a lot!

[@k4kfh]

This is incredible. I've just spent nearly a week fumbling around the internet trying to understand the Laplace transform because my professor swears up and down that he can't explain it any better "because there's no visual explanation." This was the visual explanation I needed. Thank you so much.

[@chellingiganesh6111]

3D visualisation of both Laplace & fourier clear all my barriers between Lap & Fourier. Thank u.

[@fern3436]

I'm in my last semester of electrical engineering at university. I've dealt with Laplace transforms for over a year now but I gained a much deeper understanding of the Laplace domain in just the first 2 minutes of this video. I've known how useful they are for a long time, but for whatever reason your wording finally allowed me to understand why. Thanks for making this, and the visuals were beautiful.

[@KSM94K]

How you doing now?

[@yugeshkeluskar]

In 20 minutes I learned much more than what I learned in 2 semesters of my sophomore year.

[@lonestarr1490]

Don't worry. You'll forget about all of this faster than you might think.

[@zarzisrony4656]

@@lonestarr1490 please write those down in a word file and keep.

[@Chrisratata]

He even points out in this video that you likely wouldnt learn this in class because it’s not important. What’s most important in class is where the poles are?

[@rohitbhosle6521]

@@lonestarr1490 true 🤣

[@anders5611]

So you didn't learn anything

[@ahmedelaraby7656]

I've been struggling with Fourier and Laplace for a year and this simplified everything. Thank you from the bottom of my heart.

[@balakrishnakumar1588]

I've been wondering what's the point of linking poles and zeros of control systems with transforms of signal processing. After years in dilemma, now I breath a good relief. Simply phenomenal.

[@johncgibson4720]

Super video! I applauded for $2.00 👏

[@zachstar]

Thanks!

[@bobthebuilder9416]

so glad i can just chill out and learn this w/ no time restraint

[@samueltsang9386]

The learning curve for advanced maths always seems so steep until I stumble across videos like these. Truly amazing. You explained half of my module in 20 mins.

[@GiancarloAllasia]

This is the video I was waiting for since years. Laplace transform and Fourier transform gave me a lot of uncertainties and I spent a lot of time trying to figure this out. You did an excellent job with this. Keep going man, this is the quality content that KZbin needs and deserves.

[@dol3980]

I also am a former practicing EE (Canada) and had significant issues with understanding Control Theory concepts as the intuition profered by the Prof (most of who had bad English communications skills to boot) was his text version of Bode Plots an d polls and zeroes, with no real time apps to digest like the spring DE u solved for us. I DETESTED this very "Important course because the Prof could not relate reality to Physics and probably knew less about the systems then I did at that time (my dad was a logger). Time for some real teachers of the subject in our STEM colleges not semi tenured profs with BIG egos but no real practical knowledge to impart. Keep up these great videos and what a refresher from my so mundane EE classes for the most part.

[@dol3980]

Poles and Zeroes

[@randomdude9135]

Bruh, you and 3b1b must do a collab.

[@DiamondSane]

Is it wanted to mix beer and wine?

[@radwizard]

@@DiamondSane Never drink and derive

[@Khwartz]

I can Understand your Proposal but looks to me letting having Different Approaches, Different Sensibilities and Levels, ENRICHES; uniformity would be A RISK OF LOSS OF POTENTIAL RICHESSES, in my humble opinion. So I'd rather discourage Them to do so for the Very Benefit of All Of Us All ^_^

[@kkgt6591]

No,

[@menyasavut3959]

I hope not, 3b1b has super annoying background noise (called "music"). Here, the background noise is a lot less audible, although it's still there. Honestly, I don't understand the point of adding distractive "music" to the speakers voice.

[@abioyenwankwo7308]

What was understood in class: "Laplace transform is that thing you do if some letters have more dots above them than usual"

[@YamilSG]

HAHAHAHAHA Exact words of one of my professors when he got mad cause no one was paying attention and got tired of making and effort for students that don´t care. I had to go to his office for him to explain to me personally,

[@dielaughing73]

And in the textbook for my senior-year instrumentation class: "All you need to know is: Laplace means derivatives get an s and integrals get a 1/s"

[@powerdriller4124]

That´s for mechanical engineers; we, the Electronics guys, don´t put dots on variables to represen derivatives. We use prime signs instead, and only for one semester, for all the next semesters we live in the Laplace realm, a bunch of "s´s" everyday.

[@bilkishchowdhury8318]

​@@dielaughing73Basically operational calculus.

[@americansailor7967]

Great Tutorial. As a BSEE, I learned more in a few minutes than I did in years at the university.

[@Amine-gz7gq]

it's crazy because visualization is ignored in schools and colleges

[@SachinKumar-js8yd]

Couldn't grasp it in a full semester.. you explained it in 20 mins. Awesome work bro.

[@miasix7147]

I've just learnt whole control system engineering in 20 min. respect

[@Kiran-el7ch]

I used to have a faint idea that Fourier transform and Laplace transform are linked. Thats right. This video Enlightened me about Fourier and Laplace transforms. I have a master's degree in control systems Engineering still can't understand what's the Purpose of a Laplace transform is. This video cleared All my doubts. Kudos to the makers of this video.

[@hitzcritz]

*Me:* _nods while not understanding anything_

[@skylardeslypere9909]

Hi Mr. Obama! I didn't know you were into math like this. How was it like as a president?

[@ForOrAgainstUs]

Every time a new concept is introduced that adds on to, rather than explains, the previous concept. "But of course..."

[@roberttompkins9991]

😆 almost no one gets this the 1st time. Gotta meditate on it, sleep on it, review it and try to explain it to someone else. Next thing you know, your an expert! Youse gots dis!

[@vaderdudenator1]

I’m just over here wondering what S is

[@GizmoMaltese]

@@Gideonrex1 yeah, majoring in Math or Physics is college on hard mode. They tried to teach us about Laplace transforms in sophomore year of a physics major. It made no intuitive sense to I always felt lost and confused.

[@assasin06soul]

You just Made me easily understand 2 years of University trying to understand Laplace transform, specially when everything came together in DSP this semester which I just failed. THANK YOU, please keep doing what you're doing, more people and institutions should teach the way you do

[@viniciomonge3960]

Thank you so much! You can't imagine how much time I waited for this explanation in class (and it never came) and also in KZbin. I always had this doubt about what did you win changing from Fourier to Laplace. This graphical way of describing it helped me a lot. Btw I am a graduated engineer and physics student, but with control systems and differential equations is clear that you never stop learning new things and new interpretations to things you think you understand

[@donkeydanny2114]

what are you talking about lol

[@viniciomonge3960]

I don't even know rn hahah

[@arnoldsuo7287]

this is the single coolest video I've seen this year. Zach has explained it so well that even me as a 12th grader can fully understand.

[@bassbreaker]

Great take on this! I haven't revisited the Laplace transform since college. This is a very useful intuitive understanding of the concept that tends to be masked by the mathematical rigor of academia.

[@nathan6798]

Thank you so much. You really opened my eyes to the beauty hidden behind Laplace and Fourier transforms ! We need more people like you on the internet.

[@simonstone6316]

Engineering educator here. Love the visualization and the explanations! However, I find the arbitrary use of upper and lower case letters a little unfortunate (you could say it's all over LaPlace...). The common convention in engineering is to write the time domain function in lower case, the transform in upper case, and all variables in lower case (t as well as s). correct me if I'm wrong, but you mix and match for no apparent reason.

[@hikaru-hokkyokusei]

I agree

[@Methodwake]

Fourier Information, I really enjoyed this comment. Sad laugh ensues.

[@mauriziodagradi3498]

You are right.

[@proloycodes]

@@Methodwake noo, you can't just make me die laughing in l'hospital

[@Methodwake]

@@proloycodes hopefully your health stays in acceptable limits that are determinate

[@aubreyduncan4529]

This bloke just explained almost half my degree in 20 mins. What a champ

[@rodericksibelius8472]

Wow!!!!!!!!!!!!!!!, I have been doing Electronics Technology building circuits and also have worked as a Microwave Electronics Technician for 37 years and retired now, and I am still thirsting for the understanding the physical world of why things come from. Thank You Sir for this conceptual explanation of what has baffled me for all this time. Continuous Learning throughout a lifetime is EUREKA FUN. Thank You Very Much for your TALENT of TEACHING.

[@_spartan11796]

This video would have been perfect last term when I was studying control engineering!

[@MukeshKamath]

The moment I saw the two poles in the video(keyframe) with the word Laplace transform written in title and views approaching a million... I knew it. I have finally got to something I eagerly awaited. Laplace transforms were difficult to understand in college. Just unbearable is the pain of teachers with a 2D black board to draw and explain what they perceive in their minds. Looking at the comments here I agree with most... some very funny. 7% humans who were ever born on earth are alive today. May be millions and billions more will take birth and watch this video. Out of 7% humanity alive now may be 0.07% of humanity has got an opportunity to learn engineering ever. Forget those who invented these things or knew about them but are no more alive...I bet every engineering professor who hasn't watched these kinds of videos would salivate and thirst for more.. Let alone the students. Very much appreciate the greatness of all minds which are able to comprehend these things. Just wondering where all are Laplace transforms getting applied.

[@johnped37]

This has to be the best math video I’ve ever seen. Well explained, dense in information, and understandable by experts and those only with basic math knowledge.

[@koreanfriedchildren]

This video perfectly explains why the complex numbers are refered to as REAL and IMAGINARY. So many years I have searched for this very explanation. This makes complete sense and is definitive. Thank you so much.

[@carultch]

The reason they are called imaginary numbers, is that Descartes used this term as a criticism of the idea. Out of irony, that's the term that stood the test of time, and ended up making our modern vocabulary. Gauss proposed the terms direct numbers (for what we call real numbers), and lateral numbers (for what we call imaginary numbers). A similar thing happened with the term "big bang" for the origin of the universe, where a term coined by a critic of the idea, was the one that happened to stick.

[@McPlaySpot]

My man! I've been thinking about this for quite a while.

[@dhaufjebzjchseis3828]

I LOVE YOUUUUU, I looked everywhere for an intuitive explanation of laplace transforms. I undestand what the fourier was doing but struggled to grasp laplace until this video!

[@rigorouselectronics8089]

I wish I saw these videos when I was taking analog signals and systems, and digital signal processing. Great video.

[@stefangrzech4202]

Dziękujemy.

[@sshrek1996]

Oh my fucking god! I had studied this almost like 8years ago... And I couldn't understand a bit of what I was doing! Matter of fact I didn't even realise then what's its importance... After watching this video everything is so much crystal clear. This video helps sooo much more! Infinite gratitude to the creator!!

[@saurav3078]

This is absolute gold! As a freshman taking Signals and Systems, this provides much needed intuition!

[@jlhillmann79]

ChemE here. When I took Process Dynamics and Controls (20 years ago) I never really understood Laplace transforms. I could do the math, but I didn't really understand it. And after watching this, I still don't really understand Laplace transforms and my 20 yr old PTSD has been triggered... That being said, loved all the visuals in this and how you slowly stepped through the progression. If you had been my prof, there's a chance (although certainly no guarantee) that I would have done better in the class.

[@akgille]

Really, really good work to create such accessible visuals. This is an excellent instructional resource!

[@srijansingh5198]

God bless you. I wish that from the bottom of my heart. I'm so elated after watching this video. In my college years I used to have discussions on control system with my friend Aditya and used to imagine what you so brilliantly have explained here. Every child out there deserves a teacher like you.

[@cryptic_daemon_]

Im studying Computer Engineering, and I taught this in my Circuits class, this completely changes the way I see Laplace Transform!

[@dee_zzy]

05:42 for people checking the math, there's a t missing in the laplace equation after substituting s = alpha + i•omega

[@proloycodes]

also, the next equation would lead to a t^2 in the exponent

[@gabrielcapellarisantos5946]

Wow! This is the best visualization/explanation I've seen on this subject! truly amazing!

[@juliusrobertoppenheimer9104]

Damn, This channel just keeps getting better and better

[@laurencef8535]

Explained this better than my control systems univeristy lecturer, very concise and easy to follow.

[@abcdefghijklmnopqrstuvwxyz1062]

Years of institute training wasted Now these are brand new

[@abcdefghijklmnopqrstuvwxyz1062]

My English sucks, i know. But im nơt Chinese

[@michaelsaenz380]

gachiHYPER

[@abcdefghijklmnopqrstuvwxyz1062]

This is the most liked comment i have ever had, probably because of my broken English? :)

[@Upsilong]

@@abcdefghijklmnopqrstuvwxyz1062 nah you are very right; lots of great education out there now, which does make old forms of schooling, feel wasted.

[@BoZhaoengineering]

Quân Đặng some Chinese with poor English would not approach this kind of videos.

[@MichaelCrainiciuc-jd6sc]

The best explanation in the entire youtube! Thank you!

[@JulienCope]

Amazing! Really helped understand this concept. Keep up the great content! Might get too specific but I would love a follow up video about poles, zeroes, stability and root locus (all that good controls stuff) reinforced with a real world application.

[@Mrjulianrey]

I think this is the best, and most clear explanation of the Laplace transform i´ve ever seen, thank you for having done this amazing work

[@robertdodd2087]

Studied this 45 years ago. Could do the sums and get the correct result Finally, after watching your vid, I have an idea of what was happening, thanks

[@davidho2977]

that's how I see it too.

[@yolotaylor993]

this video is awesome, finally I can understand the meaning of the laplace transform

[@mostinho7]

This video is a must for all ee We all took controls engineering, passed the exam but I think very few people actually understood why a pole on the left was stable. I sure didn’t.

[@dol3980]

Totally agree, the Profs I had (with Big egos) were more interested in imparting their math skills rather then teaching us visual control theory which we needed to gain a livelihood.

[@scottmcqueen3964]

@@dol3980 I've noticed there seem to be to kinds of engineering professors, those who like the math, and those who like its applications. The ones who like the math are terrible. Sure, everyone can pass their class, but nobody actually learns a thing while they do it.

[@INCYTER]

Outstanding work Zach. Masterfully done. Thanks. Subscribed!

[@kilogods]

This was really good, it provides intuition of the idea of the Riemann surfaces (graphs) of analytic functions. Splitting into trig and exponential sums is the polar equivalent of rotations and dilations/stretches. It’s Abelian so it doesn’t matter the order, I can rotate the plane by 30 degrees and then expand by two, or expand the whole plane by two and then rotate 30 degrees. You end in the same place. That’s analytic transformations, thought of geometrically. This is them thought of in terms of the underlying calculus and complex differential equations. It turns out to be the case in even higher dimensional complex geometry. The geometry is one side of the coin, and the other side is a bunch of complex PDEs. As a geometer I prefer and work in the geometric side because it’s easier, it’s mostly fiber bundles over semisimple Lie groups, but the analysts doing the PDE side do amazing and technical work I don’t know if I have the patience for lol. And I’m mainly talking about complex analytic geometry, where only noncompact and even dimensional geometries are allowed/ only even dimensional make sense. There’s of course the other dimensions, and that’s contact geometry and CR geometry, basic example like real analytic hypersurfaces inside complex spaces like spheres, and the boundaries of domains in C^n.

[@robertschlesinger1342]

Excellent video. Excellent refresher overview with excellent graphics.

[@farisakhtar4824]

I noticed a minor mistake at 5:21. After rewriting s as 'a+iw', the t disappears from the second line. Not important but can cause confusion for those following closely.

[@sermuns]

noticed this too. thanks!

[@nathanmoy7215]

I have been trying to understand laplace / fourier for so long and you did it in 20 minutes congrats

[@metametodo]

It's impressive how much I understood from this even though I haven't learned calculus. There were occasional things I didn't get at all, but I learned a lot just from conceptualization.

[@Amine-gz7gq]

if you can't visualize it and manipulate it, you can't understand it.

[@MikiSiguriči1389]

watched lots of material before this video, this dude unlocked meaning of this transform to me in first three minutes good job, subscribed.

[@kozhahmetisa3236]

Now I understand why camels have humps: camel drinks periodically, and the amount of water decays in its organism with time. The L-transform of that results in appearance of 2 humps or sometimes 1 hump, depending on alpha - related to genetics?

[@curiosity551]

Sorry bruh, but i laughed hard at this one 😂

[@karannakum9609]

Maybe this is deeply related with DNA in human body

[@Cherem777]

😂😂😂

[@srki22]

This is a really nice explanation of the Laplace Transform. Btw, at 5:22 you are missing t in the exponent in Laplace transform.

[@volkerblock]

a moment later t was back. Appearance from nowhere, like the virtual particles in quantum physics.

[@volkerblock]

now I've seen the video 5 times, but I have to keep interrupting the video, the beautiful pictures have to sneak into my brain and anchor there.

[@verdaylkloss4844]

I have watch video of Eugene Khutoryansky's channel and also "math and science" to understand about Laplace transform just because I just want to visualise what the heck the engineers and mathematicians are actually calculating. I admit. I study economics and law. I don't have strong mathematics background. I do study simple calculus in Economics. Now, I have basic idea of Laplace and Fourier connection. Thank you for this wonderful✨😍 presentation. You are genius ! No one had dared to explain such complicated concepts to layman with 3D. May you have great success in life... 🌿🌾💝👍😊🙏

[@7shinta7]

Great video, but I needed this 10 years ago. ^^" Well, now it's a great reminder of what I used to know in college. And it makes me a little sad considering how much I've forgotten since then.

[@ramadash2472]

I tried lots of videos to understand Z transform. This is the best and simplest.

[@pendragon7600]

Damn throwing shade on the engineers. 16:14 "Like good engineers will say if the mass is 1 then the force is 10N" oof

[@TheVivi13]

Is it really throwing shade though? Setting the mass as 1 and gravity as 10m/s^2 allows for really quick calculations as shown there. Allows for an understanding of the system with very little effort at all.

[@Blox117]

@@TheVivi13 engineering = lazy maths

[@mithunchakraborty2517]

@@Blox117 Engineering = Making things work, Even when your theory is wrong ... !!

[@TheVivi13]

@@Blox117 It's crazy how lazy maths leads to literally everything in the world around you working huh. If you REALLY think that when it actually comes to developing and building stuff, Engineers still use estimations in their designs, then you probably should go to school more.

[@Blox117]

so many butthurt engineers lmao

[@arpitgoyal3969]

You truely are gem sir... absolutely brilliant

[@sodaPapa7176]

Differential equations was easily my favorite math class

[@benjiusofficial]

The idea of rates being linked to states is super satisfying.

[@vinayj5305]

This was a very good lecture. I finally realised the great potential of learning Laplace transforms. It was difficult to learn at first in college and without the applications it seemed redundant, but you have reignited my curiosity, and for that you have my thanks. The great visualisations helped a lot.

[@Moon___man]

i just failed my laplace test today and here i am watching this lol

[@navjotsingh2251]

In order to succeed, you must learn from your failures and improve. Don’t worry, I believe in you. Just practice, practice, practice😃

[@Moon___man]

@@navjotsingh2251 Practice does indeed help! Pretty comfortable with laplace now. Now I need to prepare myself for higher level circuits classes next semester...

[@MrKen11589]

I'm a visual learner & not a big fan of complicated math, however, when you began showing the 3D references I began to understand. You explaining the math through the video helps as well. When I saw the 2D and 3D visuals in action helped me to understand the functional aspect off the problem. This video has helped me to appreciate math more, I'm able to see & understand the bigger picture. Thank you.

[@RajBhurjee]

I have no clue how I passed this course back in University. No clue.

[@rugbybeef]

Truth. I took this class as a senior in high school at a local university. I loved every minute of this material, and I have no idea now how I understood it then when 3D graphics were not nearly as available. (I'm 40 now)

[@aniruddhashinde]

Bless me too

[@mirmashrafiahasan6459]

Loved every bit of it...

[@AJ-fo3hp]

Could you kindly do samething on Wavelet transform ? This video is great,which tell insight of of laplace transform root locus

[@j.503]

This video is just too good. You (and some other KZbinrs) have revolutionized the teaching of some very difficult subjects in Math and Engineering.

[@jaikumar848]

Great video majorprep !! Really love this content and appreciate the efforts you put in for this video... could you make video on real world application of bessel function ? I heard that in Japan somebody use this to make letters on water surface ..not sure how they made it

[@AqueleGamer]

I cannot thank you enough for this video. I've taken my calc classes almost half a decade ago, and having recently been able to return to studying, this was the explanation that finally completed this huge gap that this specific subject had left in my education as an E.E undergrad.

[@OnboardG1]

"Like all good engineers we'll assume that the mass is one, so the gravity force is 10N". I too enjoy trolling physicists :P

[@poisonpotato1]

Why stop there. π=3 e=3 sin(x)=x

[@FlyNAA]

@@poisonpotato1 π=e=3sinx/x..... The Engineer's Identity

[@carultch]

Or we could gather up about a thousand miles of dirt from elsewhere in the solar system, and cover our planet. Then we can have g equal exactly 10 N/kg.

[@travism2013]

Started CS, moved to IT but still loved theory and research and math...now I'm 3yrs out of my BSci in IT and trying to move towards aerospace and robotics (mechatronics). This video seriously helps me understand why I see Laplace mentioned in robotics for Comp. Vision and how some image analysis (edge detection) is done. Very cool video, thanks for making it!

[@dragonfly9786]

0:28 he is going to assume the damping force as a 'multiple' of velocity. for those who did not understand this, it simply means F = k v.

[@cliffordwilliam3714]

Baffles me what our minds are capable of, this amazing video clears up something abstract that I could've never even imagine to visualize on a 3d model! It looks like a deck of cards as laplace with each card as fourier.

[@motmot2694]

5:20 a t is missing in the exponent of e under the integral, but a very nice video nonetheless.

[@alejandronadal6874]

This video was far more useful and well thought that my entire Superior Mathematics and Control Theory classes. I got out of those knowing nothing. Now I have a sound comprehension on the material. Thanks!

[@Grstearns]

I took Controls 15 years ago and I didn't actually understand the root locus until right now.

[@YamilSG]

I saw it 3 years ago and im happy I saw this video now and not 15 years later

[@Gouravthappa]

@@YamilSG I asked my prof the real life application of root locus and he said "in designing microchips" thats all......its like i could have googled that, fucking show me how it works dude...

[@brendanquinn6894]

I wish I had you as my maths teacher both at school and at College. Most teachers are a total waste of time just waiting to pick up a paycheck. At last I understand both the Fourier transform and the Laplace transform and it took you 20 minutes.

[@GogiRegion]

I came in knowing Fourier transforms, but left knowing Laplace transforms as well.

[@oneRella]

I've watched several videos about Laplace transforms and this is the first one to makes sense to me.

[@dominicj7977]

When you realise that 2.5 years of your 4 years in engineering can be drilled down to a just single video!!!

[@dielaughing73]

Right? Literally five semesters covering this material and today it makes more sense than ever, thanks to this video.

2.5 years of engineering school cost like over $100K

[@dominicj7977]

@ Depends on the country .

[@yamahantx7005]

I learned the Fourier transform as part of Fourier Analysis for physicists. Saw the Laplace transform as it's own math class, and it was geared towards electrical engineering. I've learned so many interesting tidbits in this video. Well done!