What is Calculus? (Mathematics)
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- เผยแพร่เมื่อ 26 มิ.ย. 2024
- What is Calculus? In this video, we give you a quick overview of calculus and introduce the limit, derivative and integral.
We begin with the question “Who invented Calculus?” Next, we talk about the two main tools you’ll study: derivatives and integrals. To understand both of these you’ll first learn about limits. After you learn how to compute the derivative and integral for basic functions and apply them to real-world problems, you’ll move up to higher dimensions and study things like “partial derivatives” and “multiple integrals.”
What to watch next:
The Tangent Line & the Derivative
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Product Rule for Derivatives
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Quotient Rule
bit.ly/QuotientRuleDer
How to Study For a Test
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How to Study Physics
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How to Study Programming
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Written and Produced by Michael Harrison
Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google as a software engineer for over 5 years before leaving to found Socratica.
You can follow Michael on Twitter: / mlh496
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Mathematics is fun, only thing we need is a good teacher.
Ye take it from a student
Yes exactly!! And maybe no teacher at all. Because some teachers simply complicate the subject and scare the hell out of students.
Exactly!
there is not good teacher get used to that idiotic school system which only make ready students for becoming good employees under big companies.
It is basically a place where you but kid brains and get a employee brain working functions for companies according to the school system and other kind things.
So we can say that there is "invisible" objects which putting your head to change your brain thinking. Maybe it is not invisible, it is the "voice" of teacher and the thing that you brain receives from that voice if we talk scientifically.
Maybe school using some form of "Gaslighting" if we think about physiologically.
The peoples who created this system didn't cared about details thats why they are succesful. Because they know that learning just 3.14 necessary than: 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 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Yeah we need a teacher that would convince us that math is fun without having to say it every four minutes of a lesson
i studied calculus 17 years back and understood the meaning today. good work mate.
mayank vaish lol
mayank vaish lol that's actually funny
That's the result of ill teached Indian education!..I also never knew that!..I wonder if any school here doesn't focus on "passing or for marks", rather focusing on the deepness of the studies
We must have had the same cluster fu@k of teachers. I got a gentleman's C at an Ivy League University because some a$$hole named, Mr. Bloom, would meet with us two or three times per week and write a proof of some theorem or other on a chalk blackboard, say, "There it is.", and then, erase it. Imagine this scene: (15) eighteen year olds and one (17) year old (me) were bringing Polaroid cameras and tape recorders to class in an attempt to keep up with this flaming a$$hole. Our average SAT scores were 1400 for the Math & Verbal duet. My father paid about $9000 for the Mr. Bloom experience. I ended up memorizing all kinds of proofs, but I had no idea how to use the integral or the derivative in Chemistry, Physics, or Economics class. When they asked those teachers, they referred me to Mr. Bloom. When I asked him, he referred me to them. My father paid about $45,000 for that experience. I have a BA & an MA, I'm a published author, and I'm a member of Mensa. Today is the first day that I ever got a coherent explanation of "What is Calculus?". Now, if I could, I would go back to my alma mater with a bullwhip and beat those teachers who conned me and robbed my father. They were a bunch of freaks and frauds. This explanation is the real deal. The bottom line is that, during a critical time of my life, I worked my ass off only to get robbed by a bunch of fakers.
fuck, everywhere it is the same situation. If things were this much clearer in schools. More students would be interested in science and we would have thousands of scientists.
I've always been really frustrated because we start learning calculus from limits, while no one ever explained to us what we were actually doing. I'm glad I watched this video before finishing highschool! Thanks a lot.
You are on a right path
The biggest frustration math students have, is not understanding what we're actually doing. Zero number sense. Just following nonsensical steps, converting this bunch of nonsense into that bunch of nonsense.
Hands down the best intro to calculus online. Not even Khan Academy or similar high-profile channels come close!
You are so kind, thank you! We're so glad you enjoyed it. We're hoping we can demystify the subject so more people will be able to understand it.
Yeah I agree, such a thorough, in-depth, and easily understandable explanation for people who haven't taken Calculus yet. I watched Khan Academy's intro before taking Calc AB, and I was super confused. Now I'm watching this well into my year of Calculus and I'm wishing I watched this intro instead
Abreviatur it is a very good explanation
@@Socratica
Sir from which country u r
Khan talks too fast as if he is spazzing out
What is Calculus? Calculus is a method of studying the complex universe by cutting them into very small pieces which turn them into SIMPLE pieces like straight lines or cubes, making them easy to apply various math. This is called DERIVATIVE. Summing all the small pieces to represent the overall picture is called INTEGRAL. Explaining Calculus as 'slope and area' merely shows the PROPERTY of Calculus. This is why many students (and general public) do not understand the fundamental concept of Calculus.
Thank you..I didn't understand what he said until I read your comment. Your explanation helps.
Makes so.much sense that way.
Thank you for this comments
I think I understand. Similar to how in drawing, you are taught to see and draw geometric shapes and how they relate each other in size and space before adding details and shading.
I have to translate subjects and ideas into art and music in order to understand them.
It's fascinating that something that appears to be extremely complex is actually made up of such simplicity. Makes you realize how important the foundations of mathematics is. Complex problems = a lot of simple shit arranged in an overwhelming way.
I’ve just done 13 weeks of maths at uni and this explained more in a few minutes than our lecturer has in months. Thank you!
UNI. You, mean the University of Northern Iowa? Went there myself, just not long enough.
@@douglasspringer1665 nah, University in general is shortened to uni in Australia
This is amazing. After a decade of rote memorization and torture, finally i get the intution. Can't thank enough. Thanks very much.
This is wonderful to hear. When you know why you're studying something, it smooths the path SO much. Thank you for watching! :)
FeelsBadMan
I am always amazed at how much clarity you have in your videos. This is absolutely golden. I love everything that you do.
That is so kind of you to say. We're so glad you are watching! :)
Jack Crawford I know right
I actually understood this
I agree, often they make it look much more complicated then it really is.
So i am glad i discovered this. :)
👏🏻👏🏻
this is one of the most clearest explanations of calculus that I've ever seen
I
I wish you were my calculus teacher.
Wow, this teacher is excellent. Clear, concise, to the point, and in a relaxed manner. Five Stars !!!
Brilliant!...I have been teaching, tutoring and using high-level math for decades and have utilized analogies and visuals since the first lesson I gave...nothing is better than quality computer animation/graphics that an individual can watch, re-watch, pause or use to explain what or where they have become lost or confused...it is sad to say that universities don't reward TEACHING, but research dollars, which is why I prefer to do part-time instruction at Community College while maintaining a career in engineering. Damn well done!
Thank you sir
Me at the beginning:
Oh, I'm probably too young for this. How will I understand anything?
Me at the end:
I am amazed
This was so great to read.
We're so glad you are watching!! :)
How old are you ?
Me at the end:
I am God
How old are you?
sirbinary pffff, fifth grader
Please, make more deeper and detail videos about differentials integrals and differential equations. Thanks
Will do! Right now we are working on in-depth videos for all of calculus. Differential equations will come a little later.
Thank you so much!
this made me subscribed to your channel :)
when will they be available ? please let me know, I am waiting. :)
George Eliozov hello George
never thought calculus was so simple and awesome.
You succeeded in combine brief and yet comprehensive idea about calculus; and that's really great!
of course I wont miss any of your calculus videos
terrific video
explained in the best possible way
This video, with its graphics and the narrator's calm, deliberate pace, is one of the best explanations of calculus I have ever seen. If only my calc professor had presented this on the first day, the pain and agony I experienced would have lessened immensely! Thank you!
I found this channel to be one of the best. Many people explain concepts with no base to plot the concept. While this channel does neither hype nor exaggerate itself to gain publicity. Teachers in here do come to the topic of interest very peacefully and explain any concept starting from its origin. This is true teaching.
I was always intimidated by calculus purely on what others were saying.
When I started it, I really enjoyed it. Along with conic sections, it was definitely a field of maths I wanted to learn more about.
It's amazing how clear and how great it is. Really deep and easy to understand. Thanks you a lot !
I regret not finding your channel before I take calculus 1 and 2. Yet, it helps me to appreciate this subject more as I review my past lessons.
I can say that the concepts in this video are very clear. As a visual learner, the animations and visuals in your videos really helped me to understand and see the big picture of calculus.
I hope that you hit more than a million of subscribers ❤❤❤
Really great video, one of the clearest explanations of calculus
Beautiful clear animations, cute little sound effects, calm and interesting voice, perfect speed, good use of repetition as well as great sound and video quality. Stunning work! I am glad I found your channel. Thank you for sharing your art.
What a kind and generous comment. Thank you so much! We're so glad you are watching! :)
Yes! Can't wait to see more of your calc vids!
Brilliant! This should be the first period of the first day of the first class of every calculus sequence!
My father taught physics at university, he couldn't explain it as comprehensive as just did.
Great work, thank you.
This is the best overview of calculus that I've seen on this site.
Hodor!
Studying this at 10th grade so I can be prepared.
That's a great idea! We're so glad you found us and are getting a head start.
LMFAOROFL!!!!
Same dude
Same :)
im in grade 9 now. im in australia we have an extra grade so if i was in america i'd be in grade 10
Excellent summary. This is the first time in my life that I've encountered a math teacher who can use English in an organized and clear way to describe differentiation and integration. Of course, I'm going to subscribe.
i have been taking calculus for four years from now , and this is my first time to fully understand why we derive or even integrate ,so thank you ,sir for this magnificent explanation :)
This is an absolutely fantastic video. Thank you so much
Thank you for watching!! :D
I love you.Like seriously.this is so clear and so simply put.I literally just reconsidered dropping out of school because of this video hehe thanks a lot
hmmm? were u gonna stay in school.. but after seeing this u wanna quit? or were u gonna quit and now ur gonna stick it out? or do u mean quit thinking about quitting or quit thinking about not quitting? i see u posted this a year ago... i'm curious, did u quit or did u didnt?
@@amandas1270 hes joking he litteraly said hehe
This is probably the best video I have watched along my mathematics career. Thank you for the clarity !!
Excellent overview of calculus. The best of several that I watched. Thanks for taking the time to share your knowledge in such a clear, concise, and helpful way.
Great job! Great videos! I'm from Brazil and studying Physics and this channel is helping me a lot! Thanks and keep the good work! :)
I Study Physics too, and I'm from Brazil.
This Channel is excelent! :)
Não tenho certeza mas acho que o pessoal do Socratica são brasileiros tbm pq tem o canal brasileiro do Socratica tbm.. eles só resolveram criar um canal gringo tbm kkkk... eu acho né... posso estar errado..
Thank you for making calculus a little less mysterious and a little more understandable for someone with no mathematical background. At least now I know what it's meant to measure, and that it's based on a few simple principles.
best explation that I have come across. It is fun when you have a good teacher. Thank you.
Really happy to see, it was the thing which I reached over and over. To do graduation was little bit difficult to understand the concepts and to co-relate how it could be, but this one made it simple and fell in for once again. Really amazing. Thank you so much for such producing videos. I request you to keep on more videos. I thank and appreciate in advance.
@Michael Harrison - I usually have to use my hearing aid when I'm trying to learn something from You Tube videos because I don't hear the higher frequencies, but your speaking voice was just perfect for me so that I didn't need my hearing aid. And thanks for not playing any background music which just messes me up.
We're so glad to read your comment. Thank you for letting us know! Access is so important.
Thank you for watching!!
And I thought I'm good at maths in school.
Looks like I have so much more to learn
Are you good at maths now ??
What an amazing explanation. I had no interest in the higher maths while in school; this definitely opened my eyes to its usefullness! Thanks and keep up the great videos!
I consider myself pretty strong in algebra (I'm wrecking it this semester, 95 in the class), and I'm taking pre-calc next semester and have no idea what to expect. I also have to take Calc 1 and Calc 2 (I'm a computer science major). Before this video, calculus was literally just a word to me. I now completely understand what I have to look forward to next fall after pre-calc. Thanks!
great video! this would have helped me a great deal when I still was ignorant of calculus.
I scraped through maths in uni, I won't lie! This is a good lesson. You guys have a great channel!
Great summary of calculus explanation in less than 10 minutes. Thanks a lot!
Thanks Michael, these videos helped me to a greater extent last semester, in a way that I could visualise the abstract operations and model them to solve real world problems effectively. I even received price of being the best business mathematics of the semester. Thanks once again, keep up the good work.
Regards :)
This is amazing to hear. Thank you so much for letting us know our videos helped - you have no idea how much that keeps us motivated. Congratulations on all your hard work paying off!! 💜🦉
This is what I needed. A good introduction to whatever the hell we are doing helps a long way in math. The teachers at my school just came in and start solving problems on the board and give assignments before leaving which we just copy from each other and the person whom we copied from either looked up the solution in the internet or he's getting private tution from someone outside the school sometimes I don't even know what chapter we are on
amazed by your explanation...We need more such videos
Me at beginning of video: Understands nothing about Calculus
Me at end of video: Understands nothings about Calculus
applejacks971
Yup, same here.
Too muck relatability
hey hii
me om _shiv_jakhar04 instagram
lets be friends
Calculus looks really interesting!
I have never heard such an explanation for which I was searching for a long time.Hats off.
That's wonderful to hear, thank you!! We're so glad you enjoyed our video. We're really hoping to de-mystify math for a lot of people. :)
Simply mind blowing... I learnt a lot in this video than my entire semester during college days
So I had a little thought. If Calculus is necessary because it's impossible to calculate the exact area of a curved surface, would this different approach work?:
1. Take any object and immerse it in paint.
2.Subtract the final volume of paint from the initial volume of paint
3. Given that the paint is thin, wouldn't the difference give a close approximation of the surface area of the immersed object? And given that Calculus is also an approximation, wouldn't this be a more intuitive method that skips a lot of the difficult math?
upload videos of vector calculus.
Not even in school or anything and this video gave me the confidence to take up learning calculus as a hobby. It's so much fun. Now I know why Newton and Liebniz were so giddy about lol
I wish people would explain why a particular aspect of math is used BEFORE teaching it.........It just makes sense.....Introducing real world examples assists also...Great job!
"text a friend each morning to see if Socratica released a new video" lol
Lol that was really funny. But I'd love to have a friend like that tbh.
This is great!!
Thanks Cassi! We're so glad to be starting this series! :)
I think we are all happy with that!!!
Very insightful! Thanks for the explanation.
What a wonderfully concise introduction to the 'big picture' of calculus.
Leibniz
Me: *spits drink*
Me: *_YOU MEAN THE COOKIES?_*
Before: Didn’t even know what Calculus was.
After: Full book of Calculus.
That’s me when I watched this video…
Best calculus I've cone across in TH-cam. thanks for sharing. Please keep uploading new videos on Calculus. It's been 2 years since you have uploaded any new videos on Calculus...
I will never forget this video and the teacher.Thank u a lot
Studying at 1st grade to get a head start
I wish I could have seen this when I was taking calculus 15 years ago. I eventually aced derivative and integral, but I NEVER understood what it was about. Just one bit of advice. Please pick an example where the answer is more random than one just for clarity. Us poor non-math brains try to read something into that that isn''t there and so it distracts.
THANK YOU! I love math with visuals. In fact I want someone to teach the whole of everything in Maths with some kind of visual! I remember when I was younger I couldn't figure out the rules of multiplying positives and negatives until I read somewhere to just imagine it on the coordinate plane. It just made sense afterwards.
A great teacher makes complex knowledge simple and accessible. Mathematics is a numerical expression of nature. Thank you for simplifying nature for us!
Please make videos on e, pi, complex nos, & undefined nos, what they actually mean in real world.
Please please please!!!
By e do you mean eulars number
*euler's
A 7th grader here trying to learn because i’m tired of gaming
I hope you're still doing this as a 10th grader. :) Learning math and science can really help you to get a good career.
I recommend this video to anyone who has to take calculus, I've done calc 1-3. The part they don't show very well in class is the visual aspect. I can crunch numbers and memorize formulas all day long but to truly learn it they should really teach it the way this guy does.
Thank you so much, Man. After watching this video I started to visualise the calculus thing. This is the best video for describing what is calculus. Your explanation is to the point. I watched a lot of videos just to know what is Calculus. This is the best of all.
What do you get when you cross a mosquito and a mountain climber?
Nothing, you can't cross vectors and scalers.
Stativemisto get out.
Ba dum tss
Stativemisto I'm so scared of the big musqiutous. I saw one today. It was in my kitchen. I dont have a kitchen anymore.
subbed to you
jajaja - not bad - i´ll pass it on
if this video was in chinese it wouldnt change a single thing in terms of what i understood or took away from it.
...Now, I know I am not the only one thinking...What?!#*?
amazing visual explanation. thank you!
Excellent clarity!
Excellent video. What I am missing is the connection between derivative and integral. It is said that integral is an inverse function to derivative. But how is "area under the curve" inverse to "slope of a curve"? I have never seen the connection...
To integrate a function, you need the find a primitive function. If you take the derivative of that primitive function, you get back the original function. Works the other way around as well.
So the integral is not really the inverse of the derivative, but primitive functions are (I think) rarely used outside of taking integrals, hence that connection.
Thanks. Sure, it's not a true inverse, since infinitely many functions can have the same derivative (e.g. x^2+C has derivative of 2x for any constant C).
Still it baffles me how differentiating an area function gives slope function. I am long from school so re-learning calculus from book - I guess understanding the relation between the two would bring a big AH-HA! ...
What Whizzer191 says above is correct. Another quite different point is that both are dependent upon the method of making smaller and smaller cuts, notionally down to infinitely small distances and areas.
In the early years of calculus, a horseshit artist named George Berkeley, a salaried do-nothing on some church payroll, claimed that calculus couldn't exist because there was no such thing as an infinitesimal. Ya gotta watch out for what these church guys try to sell you. Even if you're not a choir-boy...
It doesn't matter whether infinitely small areas exist of not. What matters is that the idea is really useful in the appropriate places.
-dlj.
Whizzer191
Yes, but why differentiating an "area function" gives "slope function" ... I never understood how the area and slope are related.
Found this on Reddit, hope it makes it intuitively clear for you:
"Rather than thinking "the integral is equal to the antiderivative," start by thinking "the derivative of the integral is the function value." The integral is area, and the derivative is rate of change. So what you're saying is that as you sweep out the area from left to right, the rate at which the area grows is directly proportional to how high the curve is at that point in time. Now it seems obvious."
I’m crying because I want to understand this but I just can’t. Math is so hard and I don’t think I’ll ever finish my degree bc of this dumb class
Best Video I understood Derivatives and Integrals in one go!!
Keep up the good work and please upload more Calculus videos
The word alone scared me. Never really understood at all what it was - Calculus. I watched this video on a whim and walked away feeling like I took the first step in opening my mind to a whole other side to what’s out there. Thanks for that!
And to think that sir isaac newton invented all of this in 1 like 1 day.
Newton is such a hero of ours. What a huge mind. :)
Socratica Newton was too arrogant.
Newton had every right to be. lol
Newton was not, he had mental breakdowns.
But whats the point of this???
dont give distorted facts, Newton discovered Calculus not invented it, this concept has been alive since the vedic times.
When I first took calculus back in school (long ago, now), the concept of what the goal of calculus IS and the initial concept of smaller & smaller rectangles were never really explained to us, making - for me - the learning of calculus very intimidating and difficult. I did poorly in calculus. Not until years later and after thinking about calculus at length did I have the required epiphany that allowed me to move ahead. Videos like this one are a wonderful resource. Thanks!
I studied calculus 25 yrs ago but really understood it only today. awesome video.
The best explaination about calculus I've ever heard...his explaination is so clear that I as a layman could start to understand...keep up the good work...
Beautiful presentation!
Beautifully done. I just stumbled on your site and will be adding it to my childrens viewing.
Thank you
Excellent video. Thanks for posting
Awesome explanation. I wish I had teachers like you.
please, don not stop ,you are amazing
Thank you so much!! Thankfully, I have a boss of mine who's encouraging me to finish my Engineering Degree, and the biggest road block for me has been Calculus. He spent about 10 mins explaining this as well, and drew it out on a napkin. When he broke it down to derivatives and integrals, it was like a light bulb went off and I started to understand why. So far anytime I've come up to Calculus I've got teachers just throwing math at us, but never really explaining why. Videos like this help break it down for how my mind works, and I'm feeling extremely confident at the moment. Especially since I finished machining which adds in the x,y, and z axes, I can even visualize and understand what you're doing for the 3d Calculus. This is exciting!
We're so excited for you!! Thank you for sharing - we think your story will inspire others, too.
This video continues to inspire my teaching. I come back and watch it again when I need a little boost. :D
I’m a freshman in high school that’s always been intimidated by calculus because I had no clue what on Earth it was but this video helped tremendously in giving me a basic understanding of it and getting rid of that intimidation. Thanks.
We're so glad you've found us! We salute your exploratory spirit!! 💜🦉
Oh my god I would've needed you 3 years ago at my freshman years in engineering. But it's fun to go back and see more clearly how things work and remind myself
We think back sometimes and imagine how great it would be to have TH-cam when we were first learning a subject. 💜🦉
i loved this VID ! Awesome fundamental explaination
Beautiful video. Great explanation
I am an engineering student and an aspiring scientist. I am glad I watched this video and I am going to watch all the videos of this series.
Superb! So much time to understand what is calculus, and one simple video resolves my problem! Many many thanks.