Calculus in a nutshell
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- čas přidán 22. 06. 2020
- What is calculus? A concoction of graphs, slopes, areas, weird symbols, and incomprehensible formulas? This 3-minute video, a submission to the Breakthrough Junior Challenge 2020, unravels the complexity of calculus by providing a (very) brief introduction to basic calculus concepts in anime-style graphics.
Topics include limits, infinitesimals, differentiation from first principles, integration.
This video is by no means aimed to teach you how to solve calculus problems, but to provide a physical intuition to basic calculus concepts.
Credits:
"Bamboo Swing, B18.wav" by InspectorJ (www.jshaw.co.uk) of Freesound.org
"Ambience, Wind Chimes, A.wav" by InspectorJ (www.jshaw.co.uk) of Freesound.org
"Wind, Realistic, A.wav" by InspectorJ (www.jshaw.co.uk) of Freesound.org
"Wind Houling 1 .wav" by Bosk1 of Freesound.org
"Seagull on beach" by squashy555 of Freesound.org
"Papers Flapping; Intense.wav" by RossBell of Freesound.org
"Chimes" by steffcaffrey of Freesound.org
"growing_plant.wav" by MaxDemianAGL of Freesound.org
"Heavy Rain" by lebaston100 of Freesound.org
"Stereo Jet Landing Sample 2.wav" by bigpickle51 of Freesound.org
"Cash Register" by kiddpark of Freesound.org
#breakthroughjuniorchallenge
bro dropped the hardest math video and thought we wouldn't notice.
Is this hard?
Are you in elementary perhaps?
EDIT:- Yes Hate me. Sorry for being honest.
@@Kay_R by hardest, I mean like its really good
@@Kay_R yeah its hard
@@Kay_R Seems like you were in elementary English class, heyy. (Though I guess my joke doesn't work since the initial comment was slang, but still obvious enough for common sense and you to not be a smart ass.)
@@Kay_R you are slow
"Even if there isn't any point in your life that you'll have to apply calculus to real life problems, isn't the ability to see the world in another language pretty amazing?"
What a banger line.
frr
factsss this just gave me a whole different perspective and view. i love when this happens.
And a life where you never learn anything new is frankly quite boring
haha.
no
If only exams were not there
Computing a very complex integral and getting an answer like 2 or something, seeing the long page of work you just did, and seeing normal people not understand anything that you wrote down makes you feel like an absolute megamind genius. That’s what’s so satisfying about Calculus to me.
Me being an asian surrounded by millions of people who can do that: "I don't feel good Mr Stark"
A omori fan in the wild
@@leozarf they’re everywhere but only show they’re Omori fans once you do something stupid like:
“Close”
Eh. Almost all slightly above average people can understand it.
@@kato_dsrdr well, at least in my country, it's not too common
My foundation for math is very basic but I wholeheartedly believe that math is fascinating. I'm always fascinated by how everything in life can be expressed in a bunch of numbers. I seriously wish schools incorporate math with real world scenarios to fully grasp the concept of it and have a very strong mathematical foundation instead of being spoon fed equations and formulas with little to no real world application.
That's elementary/middle school maths which helps you understand the high school/college maths which in turn applies in the real world.
I wish schools would adapt to the student's needs as opposed to students adapting to what the school needs. Tests and exams are fine, but when you're in 7th grade and life gets in the way and stunts your ability to learn, catching up is a nightmare as the school/teachers wont adapt to your needs. I used to excel in mathematics in elementary, I loved it. However, I did fall behind. I'm now in my senior year planning on redoing my last 2 years of high school after I graduate so I can get back into Math. Not everyone who has a desire to learn has the support needed for it, this can be Emotional or Academic support.
this is exactly what i feel! math is super fascinating and the fact that it's been so boxed into the premise of "school" and obligation that the first thing that would come up in one's mind when thinking about math is dread instead of wondrous interest just saddens me so much. i used to be the smart kid who could not do maths, and it frustrated me so much. like, days that had math in their schedules gave me so much anxiety, because i hated how i did not understand anything and how the teacher seemed to just be scrutinizing those who don't understand instead of actually helping them understand. but as i went into high school, i had different teachers, and i actually started to understand it. i realized soon enough that it was the way our education system administered such knowledge in that it kind of just spoon feeds processes and formulas without ever diving deeper into it. i feel like teachers should also understand this-that they should at least take their time to let these things marinate in our heads, because again they're so interesting and it's actually such a privilege to know of these discoveries. but then again it's mostly the way schools set such a rigid quota that it's just about reaching the quota instead of learning at this point.
now, i try to help my classmates as much as i can when they're confused or struggling with math concepts, because i know how it feels to not understand. it just makes me so sad too how this knowledge is literally just a good teacher away; some people actually think that it's impossible to understand and love math, when in reality, it actually makes so much sense. it's literally everywhere, and it's actually so beautiful. i hope someday this will change and everyone would actually get to enjoy learning as much as i have come to.
@@Nabee_H you articulated what i've exactly been feeling about our school system :( the fact that it's students adapting to the schools' needs instead of the schools adapting to the needs of the students just makes it a point that education has quite literally become a mindless routine, and it's all somehow rooted in the greed for money: education became a business. and at the end of the day, what students get is exhaustion instead of comprehension and appreciation.
Nothing stopping you of applying math to real life.
you should make more videos I think you could get pretty big, with how you explain things its pretty easy, you should try to make a Cours on this, I enjoyed this video thank you
Agreed! Too bad they stopped posting
@Niagara Falls Technician they is a pronoun..? and this voice can arguably be interpreted as a pretty gender-neutral voice, so they probably don't know the creator's gender. stop being stupid and edgy
@Niagara Falls Technician they don’t know if it’s a guy or girl so they said they, it’s that simple
I feel like yt is missing these kinds of videos which show a deep artistic appreciation for STEM over educating the audience (which you've done rlly well here too btw!) I think this video stands well on its own as a love letter to calculus
@@mauve2483 True Ted-Ed is something else but they sre a media company, not a small youtube channel who usually do everything on their own :)
This is just basic visualization of calculus. Any teacher who teaches calculation gives the exact same examples to begin with.
3Blue1Brown, cannot recommend them enough!
Look up "physics for the birds" you'll love it.
(tangent) youtube feeds you what already eat, that can sometimes become an unhealthy spiral
He dropped this video 2years ago and disappeared, imagine what beast he has become during that timeframe, because this video shows he has a very deep understanding of what he’s talking about, I pray you reach your fullest potential and have a great impact on the world to further help us understand it better.
The rate of change we see leaves us optimistic.
Are people on internet so uneducated that they think this is deep understanding of calculus? This is the example *every single teacher* gives to his/her students when he/she introduces calculus to them.
This is literally just an introduction video for calculus
@@Warlord_Megatron A) Yes actually.
B) My teacher didn't do this for me, which is too bad, because I otherwise liked her instruction style.
C) It's still nice tho. Pleasant animation, color choices and sound design. I'm down to relearn math that way.
@@normanclatcher That's a questionable teaching style. Math can't be grasped just by mugging up operations and formulas. You need to understand how to apply them in scenarios as well.
Personally it wasn’t taught to me in such a way. Yes it’s a questionable teaching style, and people are as uneducated on the internet as they are in real life, and I’m one of them.
You should look up more on how people learn maths. Pretty awfully, really.
For me who’s a simple high school country student, I had to spend great effort, multiple hours to come to this simple « rate of change » concept show in this video,back then when I studied it for the first time, no matter how simple it now looks to me.
In class no one seemed to give such a big deal about it tho. We don’t even realize that we don’t realize anything anymore.
But , It’s that kind of videos which helped me out; simple yet fundamental: the core sense of maths I would say. They gave me answers for the questions I didn’t dare to ask
pls make more videos; this gave me the motivation I needed to not completely fall apart in my first two weeks of college
Are you doing engineering?
yes. pls make more videos on calculus.
This video is so insanely well made! This deserves wayyyyy more views.
Edit: Bro this video suddenly blew up
It's impressive how you presented the motivations behind calculus in only 3 minutes. Your art is phenomenal as well. Keep on making great things!
This video is honestly so well-made that it blows my mind. I cannot appreciate it enough. Seriously.
When I took calculus almost 50 years ago, I wish someone had explained it that clearly. well done!
That was cool.
The point of learning math, at least for engineers, outside of the practical uses, is actually to learn how to think better.
Learning math allows you to understand very abstract concepts a lot better, makes your thinking process a lot more structured and organized, teaches you to analize and problem solve etc.
Also, if you manage to understand the meaning behind all the procedures and concepts, you'll gain a much deeper understanding of how the world works.
I wish I could gain this sort of understanding when it comes to math. I feel like I'm able to gain a very decent hollistic understanding on every subject, but math always eludes me. Maybe it's thanks to all those kurzgesagt , game theory, and History videos on youtube that prepared me beforehand. They grabbed these complex topics and simplified them using storytelling techniques and familiar allegories. This way, I was able to use this oversimplified abstract understanding as a "foundation" that made it much easier to understand the more complex mechanisms later.
Kurzgesagt does that with science. Exurb1a did it with philosophy. Game / Film Theory and Mark Rober did it with physics. Oversimplified did it with history. But I've yet to encounter any sort of online resource that is able to dumb down math in any sort of useful way. It's almost like there's something innate about math that makes it impossible to use storytelling techniques to explain it, it is at the same time too abstract and too precise. It's weird, I can't quite describe why. Something about math always fell off, it felt like you just used random procedures out of nowhere for no reason. I never really understand the abstract reasoning of why the procedures are used and why they work. Which is weird because that doesn't really bother me with science, but it always bothered me with math.
There's also the fact that in math you're always dealing with values that don't have any real world significance.
The numbers and variables don't actually mean anything, when you're using them in math problems you're never actually using them as symbols or standings for real world things. They always just exist in this sort of void detached from reality. At least with science, everything you learn has an observable real world effect. The concepts actually represent something in real life that you can relate to. Even if you can't see them, you understand that molecules exist. You can imagine the effects a physics equation will have on an object. But the concepts in math just represent...themselves. Maybe if we actually did more word problems and real world examples they would make sense. But math textbooks are just filled with a lot of empty problems that don't mean anything and don't symbolize any real world value...
Yeahhh I can do a lot of that and I suck at math so 🤷
@@DeathnoteBB what makes you think that you can do a lot of this?
@@marcosenarosa4877 Living…? ??? How am I supposed to answer “How I know I have skills”? I just have them, idk
no. solving actual meaningful problems is helpful, not this psychotic gibberish.
wow i was expecting an ironic video on calculus but the way you illustrated and summarized the idea behind calculus is just beautiful
I don’t have the words to explain the satisfaction of knowing that real talent is still out there. What a tremendous display. You have my respect.
Not only is the art and animation amazing, but the explanation is so well done. What a great video!
This video deserves so much more attention! I've never seen calculus as deep as this video presents it. Thank you
Maybe you've never actually studied calculus because this is what teachers teach in the first lecture of calculus.
Just an introduction video to what calculus actually is.
This explanation is literally from ANY math book. Stop complaining about your teachers and try pickup a book once in a while.
^^ wtf why are they so pretentious? this is an exceptional video, it genuinely presents the information in such an articulate and pleasing manner that even a 10 year old could understand, I've taken calculus courses and never felt inspiration to study it further than what was required but this video makes me feel encouraged to do so, I'm also grateful to the creator
There is no way this is the only video that this channel has
Man, but this is some beautiful animation and narration. I had to watch several times to appreciate the finer details - how have I missed this channel for so long? As an old artist and science geek this pretty much pushes all of my buttons! Subbed now!
Why am i only discovering this channel now? After 2 years! Bro we need more of these. Such a great video. A cute voice explaining calculus is what we need in todays world.
So happy this video is finally getting traction! My class has started out learning calculus, and I always took it for granted, but this is pretty insightful.
This was posted 2 years but it is getting recommended to people right now
Calculus took everything I learned in math and found a way to make it applicable to EVERYTHING. I didn’t believe my teachers about ‘you’ll need this when you’re older’ - but I gotta say, if my memory was wiped of Math, I would NEED to go and learn it again because it’s too cool a concept. It runs everything we do.
ok, can you explain what does it run
@@yt-sh A few examples of calculus being used are:
In the development of cars; fuel efficiency requires the measurement of different speeds of the car and other functions.
CGI in video games and movies; ray tracing, the reflection of light requires knowing how light bounces and diffuses from one surface to another
Building architecture; measuring the area of the buildings, calculus is used to prove the area of a circle, measuring buildings that are circular needs calculus
Was trying to give very specific examples, there are much more ways calculus is used, even in the same 3 fields I stated.
@@yt-sh a calculator uses Taylor and Maclaurin series to approximate the values of trig functions
42
@@thebcwonder4850 If my memory serves me right calculators don't use Taylor or Maclaurin series to approximate values of trig functions because it's memory-inefficient. Rather, they use another method, which I don't remember lol
I was absolutely SHOCKED to see that this was a submission to the Breakthrough Junior Challenge. The fact that you weren't even a FINALIST is insane. You should've WON! I've never seen somebody explain a concept so beautifully, concisely and engagingly before. The animation made it look like it was something animated by a whole team of professionals working for a multimillion dollar corporation--when I saw "Breakthrough Junior Challenge" I was blown away at the fact that you must've done all of this ALL BY YOURSELF.
My submission this year wasn't a quarter as well put together as this was and somehow I won the popular vote--so, if you're still within the age limit, I believe with all my heart that you could win with a new entry. And, even if you're ineligible by now, I'm really looking forward to seeing what you'll do in the future!!! Subscribed.
This channel has only one video and this feels like a masterpiece
THIS IS HEAVENLY! I mean the art is amazing and you explained the concept so well. Please please please make more videos!!!!!!
You've just put my thoughts and engraved memories of taking calculus classes throughout the years. Into the most simple/ visual and a bit poetic video on calculus I've seen thus far. Great job!
Whoa, wasn’t expecting such a banger video on calculus of all things in my recommendations. Your view of calculus makes the subject seem amazingly artful, and the animation in this video is so good!
Honestly one of the greatest examples of why animation is a great form of visualizing ideas aka anima to bring to life. Brilliant explanations
THIS is how they need to teach math in America. My god, you’ve done it. Nobel prize award.
If making videos like this still fits into your life please keep doing it. It’s gorgeous!
Im headed into calculus this year and honestly i was kinda scared, this really helped clear things up for me and i feel a lot more confident now, thank you!
Watching this video made me think there must be full lectures teaching calculus from basics on this channel, makes me sad that this is the only one but well atleast what is here is amazing
The video is something which is surely missing during most intro to Calculus classes.. I studied in a govt. school in India.. and most school teachers (and private tutors) were obsessed with the formulas, limits and derivatives.. no one really bothered to explain the motivation of calculus (thereby explaining the genius of Newton/Leibniz).. I developed this understanding much later in life.. when I used these principles for a living..but I often wish something as basic as this was part of the curriculum.. cheers!
Amazing video.
I ALMOST felt like I understood calculus, or COULD if the video were just a couple of minutes longer.
Keep it up!
woooow ey congrats on the first video! Amazing job with the animations. I hope you keep up the good work and cant wait to see the next one!
yo the video is amazing and directly to the point, man you're so underrated !
Akhirnya menemukan penjelasan yang paling sederhana dari kalkulus. Amazing!!!
I studied math at school, never thought it was calculus or anything serious. Exact 3 mins encapsulate 3 years : ) U did an amazing job right there. I hope your channel will grow bigger and bigger >
Hands down this is one of the best ( if not the best) math related video on CZcams!
Legal bro, muito show 👍🏻
Your artstyle is one on other hand, and it's also explained really well. I'm just sad ur submission didn't win the award (For people wondering, look at the description)
This is the best explanation of what calculus is I’ve ever heard. Good job!!
THIS SHOULD BE A TEDed VIDEO!!!! I love how this video was detailed, showing us the complexities of its topic, but also making it seem amazing and fun :)
i have no idea how this video hasn’t blown up yet. Just got recommended to me and i am pretty surprised at the quality content, keep it up math obsessed alien! 📈📈
This is an amazing explanation of the fundamentals that makes it way more interesting than any school could ever do. Love the art style too. Good video. :)
Wish that my calculus teacher had shown this video (or a similar overview) on the first day of class when I was studying engineering.
This is the best short explanation of calculus I've watched on CZcams. We need more videoooos. Seriously, even if it's only occasionally 🙂
Thank you very much for this amazing video !
By the way, it's kinda sad it's the only one of the channel. Would love to see more tbh, with this quality of animation and vulgarisation...
one of the best math videos i saw, well done
Perfect video. I imagine I would have been fascinated by it prior to taking any calculus. Now I just appreciate how well and briefly the basic concepts were summarized. :)
This is the Best Video in terms of conceptualism at explaining Calculus. Great Work !
Cuando te apasiona algo, quieres convencer a todo el mundo de lo bueno que es, no soy fan del cálculo pero admiro tu pasión para hacer que la gente vea lo interesante que es o puede llegar a ser si le das una oportunidad
I would watch all of your videos despite knowing nothing about math. I love this video. The design, the edit, your voice and your accent are pretty cool. I felt really sad when I noticed that this is the only video you have in your channel :(
This is absolutely incredible. Keep following your passion!
This is legit your only video, but damn, is this what I needed in life.
I love this video. I think it's a brilliant idea to convey STEM based videos that teach you through art. We need more of that instead of people just outright hating on STEM, especially math, just because it's difficult.
Not really difficult. Math needs time and practice just like anything else to be good at. Teenagers nowadays have attention span of 5 nano seconds which is why they cry about studies being hard.
@@Warlord_Megatron ok boomer
@@h2q8 what are you doing here bozo?
It’s difficult because for how much the system pushes STEM, they sure can’t teach it well. Us Art kids are also sort of tired of being defunded and ripped off from learning anything other than STEM. We get it. STEM is important. Guess what? So are the Humanities!
@@DeathnoteBB Huge difference between importance of art and stem
Just to realize how Isaac Newton invented calculus makes me admire its beauty and how his brilliant mind can manipulate time in order to know how quickly something changes. This is the reason why I love mathematics because it enables me to do more and to think outside the box, and with it, you can gain knowledge that allows you to understand the language of how things escalate and change over time.
Bien... no me puedo creer que subiste un gran video y te fuiste sin más
This goes so hard! I also love the cute animation! I hope you continue producing these works of art!
This is a really good intro to calculus. It’s almost like a ted ed vid. I hope you upload more videos. Maybe about trigonometry or geometry. I really wish to see more of these❤️❤️❤️
I personally think that this video is one of the most mathematical videos I have ever watched as I just got a degree.
Mannnn, that's some very good quality content. Please upload more
This was really well done! I love the animation and the explanation so much, so clear and concise. Please come back and make more math videos!
I love calculus man. Math is literally a language that breaks all barriers because it's how the world works. It's *integral* to our understanding of how everything works.
Math is the purest subject there is.
Logic, reasoning, and observations only. No subjectivity within it.
Haha lmao i got it
@@MrCrystal09 You just described the scientific process
For some, learning a new language can be hard as is learning calculus can be hard. The numbers and formulas may be easy to some but for others there is no way to get it. I get the math used for electricity and electronics but calculus wasn't in the books. This video explained calculus in a way I never thought of. Having said that, how do I learn more about the subject? I'm 64 and retired with lots of time to spend leaning new things. And I love learning.
As a student of computer science.... I love this sm, it's clearly made from heart.
that was genuinely beautiful thanks for making this!
probably one of the coolest videos out there
Where was this when I was in 11th ?
The animation is super unique!
This was an amazing video, such an elegant explanation of calculus. Please make more!
This fundamentally changed the way I thought about calculus completely and I am so thankful for it.
This deserves more attention!
This video got 99% of its views in 2 days and it’s been out for 2 years. The rate of change of views over time is not constant
Thanks captain obvious!
Hey, this was really well made! I'm deeply inspired. We need more like this. Please continue this journey of making yt videos like this.
this is my fav video about journaling on the internet
i watch it everytime i feel low ❤️
bro u explained it so well this helped me a lot
i now have a sudden urge to learn calculus
try Khan Academy videos.
Three blue one browns calculus series is incredible
Pretty sure that guy worked at Khan academy too so explains a lot
It's not that easy buddy. This video is solely an introduction to what calculus can do.
i love you for this video. genuinely appreciate you
an eloquent way of describing the derivative... beautiful
Calculus is one of my favorite math subjects. Took it for 4 years (beginer, intermediate, advanced, and in college). Definitely not one of the easiest math there is, but easier than statistics. You can't understand or solve physics without calculus. There are some problems in life that calculus is useful for.
I honestly wish schools would teach us WHY we learn maths more often. Because a lot of people have no idea why maths is useful and think it's pointless suffering, and therefore less people take it to a higher level. When I first started doing calculus at school I had no idea why it was relevant.
Took the CZcams algorithm almost 3 years but here we are and damn do I want more! Wonder if you see the appreciation or forgotten about this channel completely after all this time...
Man this video had some amazing visuals. keep it up.
This video makes it seem like math is some type of obscure media with very dedicated fandom talking about and discussing its deep story and lore and I’m honestly here for it.
and then they never made another video ever again
I love love love your art style!
well made !! this deserves way more views man, cheers!!
beautifully illustrated and very enlightening! this video was recommended at a really opportune time since I'm just starting to learn differentiation at uni lol
Gosh you're so lucky. I wish I could have found some sort of video like this one back when I was about to start my 3rd semester. Good luck on your exams!
@@notherenorthere65 thank you dearly!
You're taught calculus in University?
@@Warlord_Megatron yes, as a first year physics undergrad student I do get taught calculus. Is that weird?
@@prismaux5168 We're taught calculus in high school so it is kinda weird to see someone learning it in University.
The art is really nice for a math tutorial, if you did it great job your channel underrated! Also I still don't know anything about math even after watching it :(
Because you need to learn the basic elementary and middle school maths to understand calculus which you probably hated ;(
This person really just made an account to explain calculus in the simplest and most understandable way
your art style and explanation is amazing!
Isn't Newton the one who invented calculus
No . Calculus was invented by an indian mathematician Madhav from Kerala
No newton discovered America
@@joraversinghsingh-vo1gm now I know that ain't tru
What's going on here, huh?🧐
What are these unfunny replies?
Awesome video! Concise but still cinematic. Should've played this when we started calculus in school and then as a refresher when we get into advanced calc in engineering. Would've given me some motivation to try to beat my math demons. I consider myself lucky to have survived and aced some of the math courses in my degree. lol I definitely wasn't made for math.
I am in Computer Science and will have to take calculous at some point. This comment gives me hope.
@@JoyDavidson All the best! You'll do great if you don't listen or let others talk you into math is terrible or impossible mindset. It's just getting the understanding at the start and practicing a lot in the case of calculus which was what I have to master because of what I majored in (I don't know much about other branches, ie: stats, etc for me to tell you though). You can also start early and watch online lectures (some are hidden gem ngl) or get a good calculus book if you want a more relaxed journey throughout your degree.
yo this one actually helps when youre confused and you want to visualize it more. thanks and keep it up, hoping for more of this.
this is so good!!, i am shocked to see you have so less subscribers. I loved this video and now I am subbed!!
Calc 2 final tomorrow! Pray for me!!
Good luck buddy
@@Man-of-Steel674 thank you! I finished it!! :))
Wow, thank you so much for sharing this. I feel like the great mystery of calculus has been lifted from my life.
the animation??? the literal amount of effort which must have gone into the video???? so good omgggg
Dude dropped a single banger video and dipped off the face of the planet, been a while since we've seen channels like this ~
One of the best videos I've ever seen.