What is Calculus? (Mathematics)

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
bit.ly/TangentDerivative
Product Rule for Derivatives
bit.ly/ProductRule
Quotient Rule
bit.ly/QuotientRuleDer
How to Study For a Test
bit.ly/Study4Test
How to Study Physics
bit.ly/StudyTipsPhysics
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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[@Socratica]

Our first book is here! How to Be a Great Student ebook: amzn.to/2Lh3XSP Paperback: amzn.to/3t5jeH3 Kindle Unlimited (read for free): amzn.to/3atr8TJ

[@manjunathsanjeev5234]

Mathematics is fun, only thing we need is a good teacher.

[@karlfasselt8230]

Ye take it from a student

[@rachelrace3024]

Yes exactly!! And maybe no teacher at all. Because some teachers simply complicate the subject and scare the hell out of students.

[@dannyteachesenglish...9122]

Exactly!

[@Email5507]

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 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496 252451749399651431429809190659250937221696461515709858387410597885959772975498 930161753928468138268683868942774155991855925245953959431049972524680845987273 644695848653836736222626099124608051243884390451244136549762780797715691435997 700129616089441694868555848406353422072225828488648158456028506016842739452267 467678895252138522549954666727823986456596116354886230577456498035593634568174 324112515076069479451096596094025228879710893145669136867228748940560101503308 617928680920874760917824938589009714909675985261365549781893129784821682998948 722658804857564014270477555132379641451523746234364542858444795265867821051141 354735739523113427166102135969536231442952484937187110145765403590279934403742 007310578539062198387447808478489683321445713868751943506430218453191048481005 370614680674919278191197939952061419663428754440643745123718192179998391015919 561814675142691239748940907186494231961567945208095146550225231603881930142093 762137855956638937787083039069792077346722182562599661501421503068038447734549 202605414665925201497442850732518666002132434088190710486331734649651453905796 268561005508106658796998163574736384052571459102897064140110971206280439039759 515677157700420337869936007230558763176359421873125147120532928191826186125867 321579198414848829164470609575270695722091756711672291098169091528017350671274 858322287183520935396572512108357915136988209144421006751033467110314126711136 990865851639831501970165151168517143765761835155650884909989859982387345528331 635507647918535893226185489632132933089857064204675259070915481416549859461637 180270981994309924488957571282890592323326097299712084433573265489382391193259 746366730583604142813883032038249037589852437441702913276561809377344403070746 921120191302033038019762110110044929321516084244485963766983895228684783123552 658213144957685726243344189303968642624341077322697802807318915441101044682325 271620105265227211166039666557309254711055785376346682065310989652691862056476 931257058635662018558100729360659876486117910453348850346113657686753249441668 039626579787718556084552965412665408530614344431858676975145661406800700237877 659134401712749470420562230538994561314071127000407854733269939081454664645880 797270826683063432858785698305235808933065757406795457163775254202114955761581 400250126228594130216471550979259230990796547376125517656751357517829666454779 174501129961489030463994713296210734043751895735961458901938971311179042978285 647503203198691514028708085990480109412147221317947647772622414254854540332157 185306142288137585043063321751829798662237172159160771669254748738986654949450 114654062843366393790039769265672146385306736096571209180763832716641627488880 078692560290228472104031721186082041900042296617119637792133757511495950156604 963186294726547364252308177036751590673502350728354056704038674351362222477158 915049530984448933309634087807693259939780541934144737744184263129860809988868 741326047215695162396586457302163159819319516735381297416772947867242292465436 680098067692823828068996400482435403701416314965897940924323789690706977942236 250822168895738379862300159377647165122893578601588161755782973523344604281512 627203734314653197777416031990665541876397929334419521541341899485444734567383 162499341913181480927777103863877343177207545654532207770921201905166096280490 926360197598828161332316663652861932668633606273567630354477628035045077723554 710585954870279081435624014517180624643626794561275318134078330336254232783944 975382437205835311477119926063813346776879695970309833913077109870408591337464 144282277263465947047458784778720192771528073176790770715721344473060570073349 243693113835049316312840425121925651798069411352801314701304781643788518529092 854520116583934196562134914341595625865865570552690496520985803385072242648293 972858478316305777756068887644624824685792603953527734803048029005876075825104 747091643961362676044925627420420832085661190625454337213153595845068772460290 161876679524061634252257719542916299193064553779914037340432875262888963995879 475729174642635745525407909145135711136941091193932519107602082520261879853188 770584297259167781314969900901921169717372784768472686084900337702424291651300 500516832336435038951702989392233451722013812806965011784408745196012122859937 162313017114448464090389064495444006198690754851602632750529834918740786680881 833851022833450850486082503930213321971551843063545500766828294930413776552793 975175461395398468339363830474611996653858153842056853386218672523340283087112 328278921250771262946322956398989893582116745627010218356462201349671518819097

[@itsuzoma.5756]

Yeah we need a teacher that would convince us that math is fun without having to say it every four minutes of a lesson

[@mayankvaish1984]

i studied calculus 17 years back and understood the meaning today. good work mate.

[@apbrain1487]

mayank vaish lol

[@abdullahmoiz8151]

mayank vaish lol that's actually funny

[@rushiparmar11]

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

[@chestermicek]

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.

[@043mehdi]

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.

[@sanacy]

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.

[@mu3076]

You are on a right path

[@trentonhuggins465]

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.

[@Abreviatur]

Hands down the best intro to calculus online. Not even Khan Academy or similar high-profile channels come close!

[@Socratica]

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.

[@kedaariyer4887]

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

[@mysterium_99]

Abreviatur it is a very good explanation

[@dhananjaysahani4470]

@@Socratica Sir from which country u r

[@neohubris]

Khan talks too fast as if he is spazzing out

[@grasuh]

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.

[@imsoprettyilikepickels5561]

Thank you..I didn't understand what he said until I read your comment. Your explanation helps.

[@arbitrarylib]

Makes so.much sense that way.

[@beejay6246]

Thank you for this comments

[@WaywardPondering]

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.

[@Jacky-Poo]

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.

[@ehh.97]

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!

[@douglasspringer1665]

UNI. You, mean the University of Northern Iowa? Went there myself, just not long enough.

[@ehh.97]

@@douglasspringer1665 nah, University in general is shortened to uni in Australia

[@KevinAlexandair]

this is one of the most clearest explanations of calculus that I've ever seen

[@estelarodriguez9653]

I

[@johnhammer8668]

This is amazing. After a decade of rote memorization and torture, finally i get the intution. Can't thank enough. Thanks very much.

[@Socratica]

This is wonderful to hear. When you know why you're studying something, it smooths the path SO much. Thank you for watching! :)

[@kingjufu8308]

FeelsBadMan

[@connemignonne]

I am always amazed at how much clarity you have in your videos. This is absolutely golden. I love everything that you do.

[@Socratica]

That is so kind of you to say. We're so glad you are watching! :)

[@keamorshedsoccer1382]

Jack Crawford I know right

[@orca2276]

I actually understood this

[@HrRezpatex]

I agree, often they make it look much more complicated then it really is. So i am glad i discovered this. :)

[@brendamg7298]

👏🏻👏🏻

[@gatorbuilt]

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!

[@arbitrarylib]

Thank you sir

[@danmart1879]

Wow, this teacher is excellent. Clear, concise, to the point, and in a relaxed manner. Five Stars !!!

[@markfullilove9983]

I wish you were my calculus teacher.

[@n3r0z3r0]

Please, make more deeper and detail videos about differentials integrals and differential equations. Thanks

[@Socratica]

Will do! Right now we are working on in-depth videos for all of calculus. Differential equations will come a little later.

[@n3r0z3r0]

Thank you so much!

[@LiborTinka]

this made me subscribed to your channel :)

[@alipaf2002]

when will they be available ? please let me know, I am waiting. :)

[@apbrain1487]

George Eliozov hello George

[@darrynsanchez1713]

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 ❤❤❤

[@TomasUjhelyi]

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.

[@Albinary]

Me at the beginning: Oh, I'm probably too young for this. How will I understand anything? Me at the end: I am amazed

[@Socratica]

This was so great to read. We're so glad you are watching!! :)

[@lllegend1304]

How old are you ?

[@brandondelpesco7329]

Me at the end: I am God

[@lindsey7544]

How old are you?

[@galaticgacha-5242]

sirbinary pffff, fifth grader

[@ffhashimi]

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

[@warplanner8852]

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!

[@gauravsinha6060]

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.

[@abdullahmoiz8151]

terrific video explained in the best possible way

[@imranbug81]

never thought calculus was so simple and awesome.

[@kingjufu8308]

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!

[@emanaref7296]

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 :)

[@mamalittlefoot1491]

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.

[@Socratica]

What a kind and generous comment. Thank you so much! We're so glad you are watching! :)

[@ewiem4351]

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.

[@chuckbecker4983]

Brilliant! This should be the first period of the first day of the first class of every calculus sequence!

[@chestermicek]

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.

[@riptiderushface]

Really great video, one of the clearest explanations of calculus

[@despirithium]

It's amazing how clear and how great it is. Really deep and easy to understand. Thanks you a lot !

[@smileymcmichaels4534]

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

[@shalara6835]

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.

[@vanguard7674]

Yes! Can't wait to see more of your calc vids!

[@BensLab]

I scraped through maths in uni, I won't lie! This is a good lesson. You guys have a great channel!

[@HomeMadeBoards]

My father taught physics at university, he couldn't explain it as comprehensive as just did. Great work, thank you.

[@jlb122587]

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!

[@ageofvini]

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! :)

[@ojuliomiguel]

I Study Physics too, and I'm from Brazil. This Channel is excelent! :)

[@ageofvini]

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..

[@sighisoaraa]

This is the best overview of calculus that I've seen on this site.

[@Socratica]

Hodor!

[@JerryFochtmann]

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.

[@stefos6431]

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!

[@Nshiime]

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

[@amandas1270]

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?

[@rohanmuppa213]

@@amandas1270 hes joking he litteraly said hehe

[@A_ldo..]

A 7th grader here trying to learn because i’m tired of gaming

[@YeshuaIsTheTruth]

I hope you're still doing this as a 10th grader. :) Learning math and science can really help you to get a good career.

[@nancyayala952]

This is probably the best video I have watched along my mathematics career. Thank you for the clarity !!

[@egancurry]

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.

[@Socratica]

We're so glad you've found us! We salute your exploratory spirit!! 💜🦉

[@oldcar8592]

@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.

[@Socratica]

We're so glad to read your comment. Thank you for letting us know! Access is so important. Thank you for watching!!

[@khornebezerker7251]

Studying this at 10th grade so I can be prepared.

[@Socratica]

That's a great idea! We're so glad you found us and are getting a head start.

[@milojanis4901]

LMFAOROFL!!!!

[@adls04]

Same dude

[@racool911]

Same :)

[@somenpc]

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

[@jafrocubic2]

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!

[@Idowu_Adeleke]

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 :)

[@Socratica]

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!! 💜🦉

[@Jimmywty99]

And I thought I'm good at maths in school. Looks like I have so much more to learn

[@satvikgupta1483]

Are you good at maths now ??

[@justin60222]

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.

[@mihirchavda7791]

best explation that I have come across. It is fun when you have a good teacher. Thank you.

[@demidevil666]

great video! this would have helped me a great deal when I still was ignorant of calculus.

[@einarekeberg1672]

This is an absolutely fantastic video. Thank you so much

[@Socratica]

Thank you for watching!! :D

[@smvarunmurthy]

Best calculus I've cone across in KZbin. thanks for sharing. Please keep uploading new videos on Calculus. It's been 2 years since you have uploaded any new videos on Calculus...

[@yaoi.bl.shonenai.danmei]

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.

[@saandyyvh6682]

Calculus looks really interesting!

[@xyz2007123]

Great summary of calculus explanation in less than 10 minutes. Thanks a lot!

[@jeromemalsawmsanga8057]

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

[@prithvib8662]

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?

[@applejacks971]

Me at beginning of video: Understands nothing about Calculus Me at end of video: Understands nothings about Calculus

[@theinacircleoftheancientpu492]

applejacks971 Yup, same here.

[@akirayuripadilla451]

Too muck relatability

[@9santoshchoudhary452]

hey hii

[@9santoshchoudhary452]

me om _shiv_jakhar04 instagram

[@9santoshchoudhary452]

lets be friends

[@hendriksuryawan6924]

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...

[@ImmiTheKhan]

Simply mind blowing... I learnt a lot in this video than my entire semester during college days

[@jellovendigar]

"text a friend each morning to see if Socratica released a new video" lol

[@feynstein1004]

Lol that was really funny. But I'd love to have a friend like that tbh.

[@ionisator1]

Leibniz Me: *spits drink* Me: *_YOU MEAN THE COOKIES?_*

[@bobpourri9647]

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!

[@drewwiley7083]

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!

[@Socratica]

We're so excited for you!! Thank you for sharing - we think your story will inspire others, too.

[@dhimanroyturzo6620]

upload videos of vector calculus.

[@catplants13]

This is great!!

[@Socratica]

Thanks Cassi! We're so glad to be starting this series! :)

[@funkysagancat3295]

I think we are all happy with that!!!

[@madhurimaburagohain7438]

amazed by your explanation...We need more such videos

[@chantellegiardina5098]

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.

[@SUSsykage]

Before: Didn’t even know what Calculus was. After: Full book of Calculus. That’s me when I watched this video…

[@froellig]

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.

[@aflah7572]

Best Video I understood Derivatives and Integrals in one go!! Keep up the good work and please upload more Calculus videos

[@EagleSlightlyBetter]

This is the perfect amount of information. Parsimonious. Not a syllable more or less than necessary. Fantastic. Can you please do a series on Linear Algebra for econometrics?

[@prachi579]

Please make videos on e, pi, complex nos, & undefined nos, what they actually mean in real world. Please please please!!!

[@username2828]

By e do you mean eulars number

[@username2828]

*euler's

[@apollyon25]

Studying at 1st grade to get a head start

[@victor256in]

A great teacher makes complex knowledge simple and accessible. Mathematics is a numerical expression of nature. Thank you for simplifying nature for us!

[@ahamedimad4554]

I have never heard such an explanation for which I was searching for a long time.Hats off.

[@Socratica]

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. :)

[@koacodag]

if this video was in chinese it wouldnt change a single thing in terms of what i understood or took away from it.

[@fineartist7710]

...Now, I know I am not the only one thinking...What?!#*?

[@stativemisto3454]

What do you get when you cross a mosquito and a mountain climber? Nothing, you can't cross vectors and scalers.

[@vivekthomas8]

Stativemisto get out.

[@feynstein1004]

Ba dum tss

[@v6790]

Stativemisto I'm so scared of the big musqiutous. I saw one today. It was in my kitchen. I dont have a kitchen anymore.

[@andymattos7659]

subbed to you

[@charlesbromberick4247]

jajaja - not bad - i´ll pass it on

[@trainingporpoises.]

This video continues to inspire my teaching. I come back and watch it again when I need a little boost. :D

[@anushika01]

after 20 years since i first learnt it i have finally started to understand the CALCULUS.

[@LiborTinka]

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...

[@Whizzer]

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.

[@LiborTinka]

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! ...

[@TheDavidlloydjones]

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.

[@LiborTinka]

Whizzer191 Yes, but why differentiating an "area function" gives "slope function" ... I never understood how the area and slope are related.

[@Whizzer]

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."

[@Supplychainpapi]

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

[@ctna211]

Very insightful! Thanks for the explanation.

[@user-pu8wb4sl7d]

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.

[@Rich-bz4vk]

And to think that sir isaac newton invented all of this in 1 like 1 day.

[@Socratica]

Newton is such a hero of ours. What a huge mind. :)

[@oliverhees4076]

Socratica Newton was too arrogant.

[@adamfattal468]

Newton had every right to be. lol

[@regismystkval1871]

Newton was not, he had mental breakdowns.

[@dovahking6514]

But whats the point of this???

[@vp8577]

dont give distorted facts, Newton discovered Calculus not invented it, this concept has been alive since the vedic times.

[@TheHarveySpectre]

I studied calculus 25 yrs ago but really understood it only today. awesome video.

[@chemdah]

What a wonderfully concise introduction to the 'big picture' of calculus.

[@ahmedsabri9550]

please, don not stop ,you are amazing

[@arifalam1554]

after memorizing and calculating a lot of calculus problems for years finally it makes sense to me..... thank you for your splendid video....if you can make more videos on calculus to make sense I think it would help a lot of students like me .......

[@benjaminbaffoe3062]

You are a great teacher. It would be good to have more videos on a full calculus lesson and book. Thank you for this wonderful video.

[@ej_l2525]

this is much more clear and gives me an idea and perspective,plus the animated video makes calculus a lil bit fun and creative despite most people say Calculus is a hard subject. Im also a visual learner so this help me to step up my game.Im taking pre-calc in summer to catch up with Calc1.

[@Discovery_and_Change]

0:03 We inherited geometry from the ancient Greeks 0:08 Calculus was discovered in the late 1600s 0:27 With calculus we start with 2 questions about functions: how steep is a function at a point (use derivative) and what is the area under a region (use integral)

[@ulugbekkirgizov452]

amazing visual explanation. thank you!

[@rmasoni]

I just searched for “wtf is calculus”, as I always hear about it but had no idea, and ended up here. I have no background in mathematics, and still I believe I'm now able to at least talk about this subject. Super clarifying.

[@Socratica]

Hahahaa we need to add that to our search terms! But seriously, we're so glad we could help. Thank you for letting us know!!

[@rmasoni]

@@Socratica I did it purposefully to find a lighter take on the subject, and it worked!

[@YAakash]

i loved this VID ! Awesome fundamental explaination

[@khushividhi2713]

Your channel is very beneficial for students like me and others......I just love the way you teach the concepts...as it becomes very easy to get them ...

[@andersonmn9675]

really nicely explained. i am just starting calc 3, and it's nice to see where this is going.