Calculus -- The foundation of modern science

Easy to understand explanation of integrals and derivatives using 3D animations.

[@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.

[@En_theo]

Thanks for your video. I don't understand, at the beginning, why do we multiply distance by time ? I guess it's the total amount of work ? If yes, do we assume that the vehicle is weightless and moving in an empty space ?

[@C_Castillo]

What happen to the imigration and derogatives

[@SVent1981]

Hey. I really like your videos. You have helped me so much over the years understanding electricity. But, I have a question or a comment about the graph and how you depicted the slope of the curve after it reaches it's maximum height and starts to descend back down the y axis. You referred to it as the car starting to move backwards. That's where I have my confusion. My question is, when the curve begins to slope back towards zero on the Y wouldn't that be deceleration in the same direction rather than the car moving backwards??

[@EugeneKhutoryansky]

The acceleration or deceleration is the change in velocity with respect to time, which I did not show in this video. I was only showing the velocity and position. The velocity is the change in position with respect to time. I am glad my videos have been helpful. Thanks.

[@AjitKumar-ou4fg]

My dear , perhaps you don't know about ARYAVATTICAM GANIT or BHAHARA'S LILAVATI or BRAHMAGUPTA..... They had already used the theory of CALCULAS

[@rancidgravy2561]

with this music it felt like some kind of spiritual journey

[@1schwererziehbar1]

I'M TRIPPIN' BALLS

[@RFi731]

Because it is.

[@deshkarabhishek]

Same here lol

[@big_cuh]

Because it is, Ir F, THIS IS CALCULUS. CALCULUS.=GODLY CATFACE.

[@tafri961]

Physics is nothing but attended spirituality...

[@omniyambot9876]

Simply explained the relationship between Integral and differential calculus visually without ever mentioning technical terms. This is the fundamental theorem of calculus. Brilliant video.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@smiley235]

Wow, 8 years after dropping out of university and I have finally learned what the point of all this was.

[@kimm9086]

Exactly

[@kenapadenganchannelsaya1692]

DO?

[@tumbas299]

@@retrom well that's exactly what I'm doing

[@ChinhLe-jm1mf]

I quit high school calculus, math was boring back then, thanks to KZbin, math, science and engineering becoming a great interest in my later life. Thats why I'm here.

[@tumbas299]

@@ChinhLe-jm1mf Same here. It's interesting because now you're not being forced to learn it.

[@EugeneKhutoryansky]

If you liked this video, you can help more people find it in their search engines by clicking the like button, and writing a comment. After this video on calculus up above, I am now returning to making videos on physics. New physics videos will be coming soon.

[@godly90s87]

Physics Videos by Eugene Khutoryansky yt

[@minizahra4131]

Physics Videos by Eugene

[@ducarmelhyacinthe8598]

Physics Videos by Eugene Khutoryansky This is fuckinf awesome 😞😃😉😘😝😚😁😜😜😘😝😘😝😘😞😳😉😘😝😳😝😘😝😄😘😝😘😘😘😄😘😝😘😝😘😘😝😚😚😚😝😚😄😞😳😝😚😝😘😝😘😘😜😁😜😘😘😜😘😜😄😜😚😜😘😜😁😝😚😘😝😁😒😚😜😁💔💓💌💓💗💛💌💛💛❤💙💜💙💚💛💘💍💞💓👥💎💙😆😋😆😅😆😅😆😋😆😅😋😆😅😋😆😅😋😅😆😅😆😅😆😅😆😅😋😅😅😅 🔼🔼🔼🔼🔼🔼⬆⬆⬆🔼🔣🔼⬆🔼🔣🔼🔣🔼⬆🔼⬆🔼⬆🏫⛺💒🏩💒🏩💒🏩💒🏰🏪⛪🏨🏬🏩⛪🌆🏰🏩🏣🏩🏣🐵🐵🐵🐰🐯🐸🐶🐮🐨🐮🐒🐨🐼🐒🐮🐺🐘🐒🐮🐨🏬🏩🏬🚂🚂🚤🌅⛵✈🚤🚚🚍🚃🚈🚃🚈🚃🚈Just so good,you should. make a gaming channel so you can make physics. out of that

[@elieldushime6324]

Physics Videos by Eugene Khutoryansky Good work.but you made a mistake by failing to distinguish the distance travelled by an object and its displacement over some amount of time.they are two necessarily distinguishable concepts

[@EugeneKhutoryansky]

Eliel, thanks for the compliment. As for the distinction between distance and displacement, this is a matter of semantics. Although these words technically have distinct meanings, this is not necessarily the case in normal everyday language.

[@MikaylaTgirl]

I still can't believe that Isaac Newton created Calculus before he turned 25. Seriously one of the smartest humans to ever have lived. I have the utmost respect for the guy.

[@priyakeerthan526]

Meyaka B that too during bubonic plague. It is true that crisis brings the best out of one

[@007Sanoop]

Madhava of Sangamagrama or Isaac Newton ?

[@pagetvido1850]

+Prathmesh Tiwari That's an assumption - there are plenty of examples throughout history of different groups who derived similar or the same laws to explain the same basic rules of nature. And honestly, if it were copied it would have been done so sooner and by someone other than a college kid during the plague.

[@pagetvido1850]

+Prathmesh Tiwari But credit is given - India, the middle east, Greece and ancient Egypt were all integral parts of mathematical development. Heck, India developed the numeral system, the most widely known set of symbols today (thank goodness as Europe was using roman numerals up till then lol). Newton is perhaps more well known however (not that that has any impact in intellectual progress) thanks to developments that occurred after his achievements. These great men don't diminish each other, they're great minds reaching the same conclusions.

[@pagetvido1850]

+Prathmesh Tiwari For incandescence? There were quite a lot of people who contributed to that, of which Edison was one. Pop culture tends to over simplify things down to one figure.

[@4damskii]

I've never learned mathematics from a video and danced at the same time before.

[@nicholascureton933]

lol

[@jamesbrian2552]

Lmao

[@EugeneKhutoryansky]

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

[@EugeneKhutoryansky]

Pan Raphael Yes, Fourier transforms are on my list of future videos that I plan to make. Thanks.

[@almondjartone1206]

+Eugene Khutoryansky can you make a video on "baby math" Physics or something with standard Physics need more vids plz

[@AnstonMusic]

+Physics Videos by Eugene Khutoryansky I didn't know writing a comment was considered in the search algorithms. Interesting.

[@aroseland1]

+Physics Videos by Eugene Khutoryansky Hahahah that is so the way a mathematician would market a video.

[@jeromeeuler168]

+Physics Videos by Eugene Khutoryansky That would be amazing quantum mechanics is gonna revolutionize physics.

[@ArthurMorganFTW_RDR]

I am absolutely speechless, I mean with the help of this 20 min video I can understand like half of my textbook...

[@lamzez94]

I wanted to correct something. I think what you explain in the video as "distance traveled" is actually the displacement. The distance traveled would be the sum of the area of every rectangle, doesn't matter if it's a negative or positive.

[@rawandmahmood9368]

Exactly. I wanted to comment the same correction.

[@akkshay1992]

yes ....because the distance traveled is irrespective of the direction of travel...it's the total movement of the object

[@pepegasadge2977]

Is it? Isn't it the area under the velocty vs time curve that is the total distance travelled? Not under the position vs time curve?

[@huseyince9195]

o it is wrone. This videos are real :) and i hope come come come...

[@golaibano8291]

Celeritas you r ri8

[@henrythompson3991]

Thank you. I know your series is about physics, but this one was an eye opener for me. Calculus is a subject I never studied and my math fundamentals are terrible. Your presentation made calculus something meaningful to me. I only wish I had this understanding while in school. I didn't realize how enjoyable studying math or physics could be.

[@EugeneKhutoryansky]

+Henry Thompson, I am glad that you found my video helpful and enjoyable. Thanks.

[@MichaelHarrisIreland]

Tks, this video helped me a lot to understand what calculus is about. An absolutely beautiful and simple presentation I'm so thankful for. Saves a lot of grey cells for an old man in a hurry.

[@EugeneKhutoryansky]

+Michael Harris, I am glad that my video was helpful. Thanks.

[@user-ll7kq7ne4d]

+Michael Harris salute you !

[@sensey01]

Can you explain me, why at the end the integral was the distance and not the whole are of under f? Im asking because in School I ve learned that the integral describes the whole area under f(x). In this video it was rather the distance.

[@oasisrai4135]

@@sensey01 HEY, it's already clearly said in video that area also happens to be distance by using formula. Have a nice day :)

[@sensey01]

@@oasisrai4135 thank you for clarifying 🙏

[@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=rjLJIVoQxz4&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.

[@jaelsonnen5750]

Not as good as trig one, but not bad either.

[@manaskumar4950]

Gr8

[@ubeydans258]

can i add the turkish subtitle?

[@EugeneKhutoryansky]

Ubeyda, this video already has Turkish subtitles. But, it doesn't yet have a Turkish translation for the Title / Description, which you can add through the link above. By the way, to see the subtitles, 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).

[@timuvlad6764]

Great work for the entire Chanel not just this video, what software are you using?

[@ainnovation6967]

I was once called Mathematician and human calculator when I was still in school, being top in mathematics in the class and seeing this brilliant mathematics animation, I feel like want to teach and follow your step. I wish the young generation students will find your channel and I will keep recommending your video when some folks asking me about math.

[@EugeneKhutoryansky]

Thanks.

[@instruraja]

I cannot thank you enough for putting basic concepts in a detailed manner. thank you very much

[@EugeneKhutoryansky]

Glad you liked my video. Thanks.

[@bindulamichhane8870]

thank you so much

[@bharatvats]

Physics Videos by Eugene Khutoryansky thank you Soo much

[@big_cuh]

@@EugeneKhutoryansky :3

[@ishworshrestha3559]

Yew

[@cartsoel9652]

As a visual learner and someone with ADHD and Autism I really appreciate the pace of the animation. It’s helpful to me to see the whole idea seen through to completion even if it seems redundant. I benefit from having core ideas repeated as they become more complex with each iteration. It makes it easier to digest and grasp and visualize. Very helpful. I also appreciate the simplicity. I have trouble sorting out which Information is useful or not. The only information shown in the animation and narration was the information necessary to understand the current idea. Thanks! More Education needs to be like your videos. It should be as easy as possible to learn things regardless of who you are or how your brain works. You do a good job at that.

[@EugeneKhutoryansky]

Thanks for the compliments.

[@Aeroprism]

I still can't believe you put my songs in there. Makes it all hard for me to focus on all the science! Truly great videos, been a fan of this channel for years! Thanks you sir for helping us learn! And you can use more of my music whenever you like! I have lots I haven't even posted on my channel if you need more.

[@EugeneKhutoryansky]

Thanks. I love all your music. I listen to it very frequently.

[@unotechrih8040]

If that is your song that starts at 6:30, please upload that or let us know where we can get it. It's incredible!

[@Aeroprism]

@@unotechrih8040 Yup, all mine. I changed webhosts recently and my whole website had to be remade, for now only my game remixes are up. I guess I'll need to put my originals as well :) www.nekoprism.com

[@unotechrih8040]

@@Aeroprism you definitely should! This is really good stuff! Keep up the good work! 👍

[@Isidora14ossandon]

@@EugeneKhutoryansky Thanks a lot because of you I have regained my faith in human cooperation. I cried.

[@frankr.6571]

When we think of math we remember from grade school lots of memorization to turn one self into a human calculator and in doing so ,we missed out on the visual beauty of math.

[@pourliver]

This made so much sense! As someone who will take calculus classes very soon, I really want to thank you for these clear explanations!

[@killuazoldyck3839]

Wow 6 years ago I hope you did well

[@sf4Guy]

Now I understand the real world application of calculus. Great video and explanation. High schools and colleges need to incorporate your video into their calculus lesson so students can be more excited about its real world application and not be bored out of their mind. My college days of taking calculus was passing the tests and exams, but never understood the application to real world. Took physics and got lost in applying calculus to it.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@rango-konk]

I love this!!! I firmly believe that there are certain things in our universe we simply struggle to explain with words!! Words aren't enough!!!! We just need a different sense of approach and perception to understand it!!!

[@bobmathews4557]

I struggled through calculus in college. I passed the class, but had no idea what I was doing. I wish I had seen this video years ago. Thanks! This is a great video.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@mikexhotmail]

With all that music from 6:35 I can imagine the whole class raving together with the teacher while mumbling " DY divide by DX is a slope and Calculus is pretty dope "

[@StyrofoamCancer]

Great visualization exercise, seriously helpful to those who are just wetting their feet in the subject.

[@carterminter7814]

Thank you so much for taking the time to create this video. I was filled with an unbridled joy and rush of adrenaline as the relation of traversing distance and time correlate mathematically to area and slope. This style of teaching should be implemented in all early calculus instruction.

[@EugeneKhutoryansky]

+Carter Minter, I am glad that you liked my video. Thanks for the compliment.

[@MrFernandoBedoya]

From time immemoral I have been looking for this light!

[@mohannadwazwaz4715]

كل الشكر على هذه الأعمال الرائعة

[@thelanner22b]

Finally Understood The Idea of Integration. Thanks.

[@EugeneKhutoryansky]

Glad I was able to help.

[@thefarmer4586]

I don't know how to thank you, but I just need to know, how on earth do they teach us the integration without introducing the meaning of integration first as you did here. now I have a feeling that I need to go through all the equations that I learnt before that included integration. THANKS

[@vahangood5999]

@@thefarmer4586 Well, now they can incorporate this video in every into to the Calculus' class.

[@sensey01]

Can you explain me, why at the end the integral was the distance and not the whole are of under f? Im asking because in School I ve learned that the integral describes the whole area under f(x). In this video it was rather the distance.

[@raXunHAWK]

Mam, I really don't have any words to THANK YOU for this and for every video that you have made so far!! You're doing an outstanding job! Your way of teaching is simply MARVELOUS!! I just LOVE it! Yours is the BEST CHANNEL in whole of KZbin and you are the BEST ONLINE TEACHER I've ever had. Complete RESPECT for you :-) :-)

[@EugeneKhutoryansky]

raXunHAWK Thanks for that really great compliment. That is really nice to hear, and I am glad that you like my videos that much.

[@raXunHAWK]

The pleasure is all mine, mam! God bless you. :-)

[@skhotzim_bacon]

Haha I'm pretty sure that Eugene is in fact a Sir

[@stevemackelprang8472]

Outstanding! I wish this would have been available 50 years ago. Thank you for your efforts!

[@EugeneKhutoryansky]

Thanks.

[@b00gi3]

Perhaps one of the top 10 most amazing channels on yt. Love it.

[@EugeneKhutoryansky]

Thanks.

[@arsicjovan9171]

Just so you know, your efforts to read and answer as meny comments as posible is highly aprichiated!

[@EugeneKhutoryansky]

Thanks.

[@dann3410]

These videos by Eugene are solid gold. The narration is outstanding, among the best on KZbin and suitable for commercial use. The graphics are amazing.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@prachi579]

Your work is very detailed. I mean the balls showing reflection & the watch showing exactly the number where it reaches on time axis......... You really worked hard for it. Thank you

[@EugeneKhutoryansky]

Thanks for the compliment.

[@abhijitmandal5221]

Word is not enough to express how simple and beautiful the video is.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@NORIWAKI83]

Tremendo! Buenísimo! Enhorabuena por el trabajo, una verdadera obra de arte.

[@hardiamin4485]

i understood what calculus really is for the very first time.. thankyou so much . you make great videos

[@EugeneKhutoryansky]

Glad you like my videos. Thanks.

[@akrhsahn]

Real nice...I just wished someone would have made me understand this way in my school and college grades...wonderful. Keep the good work going.

[@EugeneKhutoryansky]

Arshi Khan Thanks. I am glad you liked it.

[@EighteenYearAccount]

I think it is dumb that in school they only teach you the skills and not the underlying theory, because with the theory you can derive everything else and understand the skills so muchh more easily

[@Ajot619]

Simply awesome ! Great job (y)

[@robertferraro236]

Speechless about the clarity with which the concept is presented.

[@MidoriKizaki]

This is simply amazing. Everything makes sense now... THANK YOU SO MUCH! P.S. I decided to become a patron of yours :P

[@EugeneKhutoryansky]

+ChunQing Yin, I really appreciate your support and I am very glad to have you as a patron. And thanks for the compliment about my video.

[@3deeguy]

Thank you. I kicked myself because I never took calculus in high school but it never would have been as clear as this. It's illustrated in simple terms and I can stop the video at each point to let it sink in. I also studied your video on FFT's because I want to understand Goertzel's algorithm.

[@jayocaine2946]

its a lot more complicated than this haha

[@oliverodinbordas4517]

You, Sir, are a genius, and far better than some college teachers out there... This, and your numerous other videos are awesome!!!! Huge respect from Hungary!

[@sulayman960]

Thank you for all your videos.....Excellent.

[@BentHestad]

Your videos are amazing man, my deepest respect for your work and my highest recommandation! May I ask what your background is?

[@b00gi3]

He has a website with all his info on it. You can find it pretty easily on the google.

[@jdean2131]

Outstanding lecture/video. Very well done!

[@EugeneKhutoryansky]

***** Thanks. I am glad you liked it.

[@carlosloures2436]

Excellent Video. Understanding the things is the best way to learn.

[@mubafaw]

Wow! Had to take several screenshots at various timestamps! Thank you so much 😊 You have done your bit for humanity! 😊🤗🙏

[@rzrbck84]

These videos are always so good. I wish they were around when I was an Undergrad,lol. Subscribed :-)

[@EugeneKhutoryansky]

Thanks. I am glad you like them.

[@totalfreedom45]

“The integral of the graph of the speed will always be equal to the distance traveled. This is the fundamental theorem of calculus.” Wow! Thank you, Eugene Khutoryansky and Kira Vincent! In 17:59 minutes, summarized in 23 words and using clear, beautiful 3D animations you have given the best, briefest definition of the core of calculus, the most powerful tool ever invented by the human mind to handle physical reality. Leibniz and Newton would’ve been very happy watching this video….😊

[@EugeneKhutoryansky]

totalfreedom45 Glad you liked my video. Thanks.

[@TheDavidlloydjones]

Wow indeed! No. That is not the fundamental theorem of calculus. It is one of the few odd phrases in this terrible video which happens by accident to be correct, but it is not the fundamental theorem of calculus (which I suggest you google up, to see Eurene's error in depth.)

[@Mysoi123]

@@TheDavidlloydjones en.m.wikipedia.org/wiki/Fundamental_theorem_of_calculus What Wikipedia stated totally agrees with Eugene on the fundamental theorem of calculus.

[@computeraddiction7082]

Appreciate your video.great graphics,great explanation.Everything is just perfect

[@chrisf8530]

There are some crazy deep connections here that I never realized until this visualization. Thank you so much for your efforts!

[@EugeneKhutoryansky]

Thanks. I am glad my video was helpful.

[@TheKaushal8686]

Wish this was created during my school days...I would be a genius.... :D

[@knighth2068]

Lol I love the music you used for this video. Sounds like it came from action movie and this is supposed to be a math video 😂😂😂😂😂😃😀😀😇

[@alexk.7064]

That was the most interesting video on mathematics I've ever seen. Thank you for helping me understand the stuff im being taught in high school.

[@swapnalidhawale3270]

I was so happy when I finally understood this Thanks Eugene

[@aentropy]

Great video but I advise everyone to watch it at 1.25 or 1.5 speed.

[@xmanxmansyr3147]

Yeah.. I watched at 1.75.. ;-)

[@kirafortherescue7756]

*I advise not to.*

[@barbarannop1799]

Badr Yasuo it is hypnotizing and you almost fall asleep if you dont speed it up

[@SteakBarker]

Great video. I liked it a lot, but not as much as that video on string theory I haven't watched yet. *wink*

[@JohnJohnson-hl4fv]

Your video has got me excited about calculus. All I can say is WOW!!!!!

[@MarcoAntonioCenturion]

your videos are simply incredible. You has such a great patience on doing this. Great!

[@ckpsolutions7300]

Can you please make a video on difference between differentiation and variation of a function

[@Iamreal11xingping]

when the car is travelling backwards, why are you deducting the distance traveled backward by the car.... distance is scalar, displacement is what u should have mentioned

[@TheDavidlloydjones]

Correct. And the yellow and green of the areas do not mean what the voice-over says they mean. That whole discussion is riddled with error.

[@abdulrenas3249]

May be the video maker would have presumed that everyone may not be aware of the disparity between distance and displacement

[@big_cuh]

That was relative to a certain direction, causing the mistake.

[@southernkatrina8161]

His odometer definitely shows he made distance!

[@carultch]

@@southernkatrina8161 Not all odometers measure a secure-forward account of total distance traveled. On modern cars, with electronic odometers, they do. Electronic odometers count forward, regardless of whether the car is in drive or reverse. But mechanical odometers were never built to work that way. The original mechanical odometers that cars had, would spin backwards while the car is in reverse. The underlying assumption is that you never drive a significant distance in reverse to make a noticeable difference in the car's wear and tear that would impact its resale value. Some cars would etch the digits as a countermeasure to tampering, so that if a Ferris Bueller style of odometer fraud is attempted, there would be evidence of it. On the car Ferris Bueller was driving, the odometer will spin both ways. The reason the miles didn't come off the odometer, is that the pickups for the odometer were on the front wheels of the rear wheel drive car. So he'd have to manually spin the unpowered wheels, to take miles off the odometer. Another countermeasure to tampering in odometers, is a directional clutch. Such an odometer would use this clutch to disconnect the shafts, when the car is in reverse, and re-connect when the car is moving forward. You could drive in reverse and never add or subtract a single mile to the odometer.

[@marcoantoniogarcia1910]

Muy buen video. Excelente manera de educar. Gracias.

[@dawei53]

this is the best video I've come across. The animations help me to get my head around the whole thing - thank you.

[@EugeneKhutoryansky]

dawei53 Glad to hear that you liked it that much. Thanks.

[@huihui666]

OMG.. U ARE AMAZING!! I really love your work and i hope you make more videos. The way your using 3d animations to explain complex concepts is amazing...

[@EugeneKhutoryansky]

xihai luo Thanks for the compliment. More videos are on their way. I am working on the next one right now.

[@TheDavidlloydjones]

"Hi Bye," This is true. Most of Eugene's work is superb. Most of it is also correct. This video happens to be an exception from his usually excellent rule.

[@DavidRamirez-mi5pp]

Minus the theme music from sonic and you've got a great video lol

[@earledaniels4539]

The incredible graphics makes understanding the theory easier. Mathematics was one of my strongest subjects at school but we didn't have these great learning tools which are readily available these days.

[@titus2744]

Really nice animation and explanation, best i have come across.

[@amvhighlights89]

4:41 Rectangle : I'm no more rectangle

[@fediarfaoui9194]

excellent video thank you

[@EugeneKhutoryansky]

+Fedi Arfaoui, You are welcome, and thanks.

[@Diedeux]

+Physics Videos by Eugene Khutoryansky Excuse me, what music did you use for this video?

[@khyatishah1452]

nice video. Easy to understand. waiting for more videos like this. Thanks

[@Reach3DPrinters]

My journey into knowledge continues. Thanks again.

[@marco1824]

Liked and commenting. Your videos are really cool!

[@EugeneKhutoryansky]

+Marco Martín, thanks.

[@rickiquartz5661]

The best explanation I ever read/see. Thank you very much for doing this video.

[@EugeneKhutoryansky]

Ricki Quartz Thanks. I am glad you liked it.

[@MrYbhushan]

Great video.... Wish I had something like this during my school days. Well it's never too late to solidify the foundation.

[@joesamalis]

What an excellent teaching tool. The best I've ever seen.

[@EugeneKhutoryansky]

Thanks. I am glad you liked it.

[@michaelmcneil4168]

Imagine being stuck in front of this screen and having to pay attention for the duration. X=zzzz

[@weblixinstallers8082]

What's the music at 3:39, 10:26, 12:54, and 16:21? Thanks in advance! :D

[@crash7855]

Tell me if you find out please!

[@u-ser530]

You can find most of them just google 'Nekoprism'

[@awawpogi3036]

Darude - Sandstorm

[@phandl031247]

The video is a great teaching tool as well as a way to review the concept of calculus.

[@justinlagasca5430]

These(all your videos in your channel) are the only tutorials that no matter how complex the concepts are, you will still enjoy the journey. The animation and good choice of background and well narrated information are ....I cant say the exact words but I'm really thankful for your efforts to make learning more fun and at this time where the pandemic force everyone stay at home and lost actual learning experiences especially hands on, your videos are a versatile platform of learning. Even though I cant do hands on learning because of the danger of the virus, your videos has helped me visualize my subjects in a clearer perspective of understanding. Thank you so much! Stay safe.

[@EugeneKhutoryansky]

Thanks. I am glad my videos are helpful.

[@memeswereablessingfromthel3942]

Music making me feel like playing Runescape

[@anastasiadunbar5246]

7:53 dat dividing animation

[@confused6526]

Nice presentation and animation. Thanks

[@chiranjitganesh1893]

Wow wow wow!! Thank you!! Love from India!!❤️❤️

[@prasetyotrihadianto4805]

A very helpful video...

[@Gamesational1]

I am literally god now.

[@berhanuget]

When I left my studies has passed a lot of time; God thanks I have arrived in this Technological period & see your magical works. I have liked Maths from the first beginning of school. Thank You Very Much. It's really SUPERB

[@justincase4812]

The visualizations really manifest my understanding of the concepts here.

[@AhnafAbdullah]

What's the music at 7:18?

[@AhnafAbdullah]

What's the music at 7:18? Please and thank you

[@EugeneKhutoryansky]

"Undreamed" by Nekoprism. You can download it for free from his website. Just type "Nekoprism" into Google.

[@RamjetX]

So thats what the squiggly S is for!

[@709zzy]

Lol that little clock on the x axis actually have the pointer pointing at the corresponding time. You really spent effort for making these videos. Thanks!

[@santelmo5222]

Thank you so much! I've been having trouble conceptualizing what I'm studying in calculus right now and this video really helped! I also liked your video on entropy!

[@vaibhav3638]

7:10 thats displacement not Distance Distance is total path traveled

[@Mysoi123]

According to the fundamental theorem of calculus, if the endpoint we select yields a value in the function, then that is the highest value attained since the start. This is akin to traversing a peculiar, curvaceous path around a gravitational field, where the work done only relies on the initial and endpoint locations.

[@RobbieHatley]

I really liked the final 10 minutes of your video. However, I found the first 10 minutes over-simplified to the point of causing confusion rather than elucidation. You're straying past merely "simplifying" to the point of "talking down". I suggest that the video would be better with most of the first 10 minutes simply removed. Cut the introductory material to a minimum, or you risk so boring your audience during the FIRST 10 minutes that they may turn off the video before it gets to the interesting parts in the SECOND 10 minutes. Perhaps condense the first 10 minutes down to about 2.

[@fernandogalvao8661]

***** bla, bla...

[@RobbieHatley]

Fernando Galvao : If you don't read English, I suggest Google Translate. That way things won't seem "bla bla" to you. (Provided, of course, that you have a functional mind, and that you can read at least one commonly-used written human language fluently.) translate.google.com/

[@j.jcagney6522]

***** You are wrong. She did it the best she could do,some students do not understand or know even the first ten minutes. She knew perfectly where she begins and where she ends. I believe if this lady taught a donkey with this way,it will be a scientist in calculus in short time..

[@Sough]

***** I agree. You can't do everything in one video. If you keep the first 5 or 10 minutes, you might as well explain integers, addition, multiplication, etc. If someone can read a graph with a Y axis, most of the rectangle use just gets in the way.

[@yasirbadmos2110]

+Robbie Hatley I agree with you....but it is only boring because you already know it. The whole video is good as it is for public consumption. Just as we have a 'brilliant you' so do we have a 'dull me'...

[@victorsanchez5939]

Simplemente sublime. Excelente manera de explicar lo que es el calculo. Saludos desde México.

[@mlw2377]

Mr. Khutoryansky, I have always wanted to under stand this in DEPTH not, just pluging in number. For the first time now I do. Thank you so much for making these videos.

[@EugeneKhutoryansky]

+C Saucedo, you are welcome and thanks.

[@alb4599]

Nooooo! Call it velocity! Not speed! A wonderful presentation otherwise!

[@mjtsquared]

Well the graph isn't showing the direction of movement anyway like a scalar.

[@55chh]

maybe leave out the corny music?

[@walkingowl6810]

The music is also part of the foundation of modern science

[@709zzy]

maybe you can leave out your opinion?

[@whoatemyhummus]

Music is math.

[@maxbooth6247]

I love the music in this

[@ooloncolluphid7904]

Would you prefer Grand Ole Opry? Tech N9ne? Ooo, how about a little Slipknot? That'd help us concentrate, wouldn't it?

[@mrbreakybee]

Magnificent! It's far beyond what I expected.

[@EugeneKhutoryansky]

Thanks. I am glad you liked it.

[@somphol]

Awesome explanation, thanks for making this so accessible!