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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
http://bit.ly/TangentDerivative
Product Rule for Derivatives
http://bit.ly/ProductRule
Quotient Rule
http://bit.ly/QuotientRuleDer
How to Study For a Test
http://bit.ly/Study4Test
How to Study Physics
http://bit.ly/StudyTipsPhysics
How to Study Programming
http://bit.ly/Learn_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 for over 5 years before leaving to found Socratica.
You can follow Michael on Twitter @mlh496
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Text Comments (627)
## Would you like to comment?

Emad Rahi (2 days ago)

how can you edit your videos ? what software do you use?

king jufu (5 days ago)

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!

Ben Stone (7 days ago)

Dope video. Currently in trigonometry/ pre calculus. Will take next year

MLG Player (11 days ago)

Ah the thing i wonte study i hat math

Sanam Khan (12 days ago)

Oh I just completed 10k likes in 10 October 2018

Md Bahar (24 days ago)

Great teacher, God bless you dear.

Research (25 days ago)

I wish I never did drugs!

GrumpyOldMan (27 days ago)

Why did the derivative have to be 1? That's just a very exceptional case. Unnecessarily confusing.

qualquan (1 month ago)

just conventional stuff
no special insight
besides integration is more than finding areas since it can find volume and line (height).
no critical discussion of differentiation.

Sandy (1 month ago)

Tell me how many of you watched this video because calculus is now, used in AI and machine learning XD :)

Jeremy Metcalf (1 month ago)

Where were the other two slices in the beginning? I only counted eight.

Veronica Worthen (1 month ago)

Your video was amazing! I was able to understand everything so well

stonent (1 month ago)

Funny thing is I could easily write a program to calculate this, but doing it the math way is difficult. In my Physics class I wrote powershell scripts in class on my laptop to do physics calculations so I could plug in numbers and get answers. The instructor seemed impressed.

anuradha dhananjaya (1 month ago)

It was a great explanation. Thanks

John Batchler (1 month ago)

We're ever there is x replace it with-1

John Batchler (1 month ago)

U have to how to use it and when to use it to see the whole picture as long with the rest of other maths

Sridhar K (1 month ago)

Good Work !!!

Mantej Singh Dhanjal (1 month ago)

What are the real world examples of Calculus?

anjali Dass (1 month ago)

How did u find the area of the rectangles in the integral????its not clear to me pls tell me 😣😣😣😣

Prithvi Sundar (1 month ago)

Yeah I've been studying Calculus not even knowing what it is. Thanks bro

Namah Shrestha (1 month ago)

One video has more worth than a month of my calculus class ever had.wow

Ayush Singh (1 month ago)

i am in 9

subith sjohn (1 month ago)

This is too complicated for me but are really good

Alexander Kenny Wen (2 months ago)

Quality Content!

J (2 months ago)

I wish you were my calculus professor

Ramesh Reddy (2 months ago)

Sir do more videos on calculas we are waiting

Derec Wilsom (2 months ago)

Very nice intro

Blue Hamster of Redemption (2 months ago)

It would be nice to get names of presenters, or their 'nom de...videos' (?) so we could refer more directly with the presenter. The woman presenting awesomely hilarious and effective Python vids would become 'Salima' rather than 'the hot chick in blue', and the calculus presenter would be 'George' rather than the 'dude who explains skinny rectangles in calculus'. In either case, more hilarious hot-chick Python vids and more 'skinny rectangle dude' calculus videos please!

Socratica (2 months ago)

Hmm. If only there was a description box for videos where you could find more information.
:) Thanks for watching!

Stefos (2 months ago)

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!

BENJAMIN BAFFOE (2 months ago)

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.

Antariksh Mukherjee (2 months ago)

I am from India and im in the seventh grade right now. This video clarified my doubts to what I will face in my higher studies.

h4rder10 (2 months ago)

how do we find the function itself? this is bugging me. i mean in real life we have to determine the function and the curve right? how do we do it? derivative and integral tells us about what to do AFTER getting the function/equation. but my question is how do we develop the equation or function from say a car travelling at different speeds over a course of time.

Simon N (2 months ago)

I've studied this for months but I didn't know that it was called calculus....

johnpro2 (2 months ago)

function ? does it mean the graph line described in algebra notion ?

NIRMALYA SENGUPTA (2 months ago)

Excellent video!!!

sreereka baskaran (2 months ago)

You are great,thank you sir

Satish Pandu (2 months ago)

absolutely amazing.... worth watching.... thanks

Jonathan Haddad (2 months ago)

congrats you just taught a 15 year old Calculus

Souvik Dey (3 months ago)

Super sir..love from India 🇮🇳🇮🇳🇮🇳

Serin S (3 months ago)

Why am I watching this? I'm only at first year highschool..

darkdoctor2017 (3 months ago)

They discovered or they invented ?

WebDev (3 months ago)

Thank you very much!

REGIL TUBE (3 months ago)

I hate mathematics it drive me crazy thru my scholar life. ahhh i wish i could kill those people who invented much more complex branches of mathematics.

magesh lakshmi (3 months ago)

Fantastic

shamusfarmer (3 months ago)

Nope.

Sakshat Karandikar (4 months ago)

Ha ha calculus was invented in india

KRIPA SHANKAR SHUKLA (4 months ago)

Totally amazing explanation!! THANKS A LOTTTTTTTTTTTTTTT!!

Chelle Weatherspoon (4 months ago)

Wow! This was really helpful.

Arpita Sarkar (4 months ago)

NC explained

HIMESH VIEWS (4 months ago)

Which editing software please tell me sir

Mycroft Holmes (4 months ago)

I want to cry. How can you find this interesting?

Arjekay (4 months ago)

Awesome, this was so refreshing and gave me back the big picture

GGGames 101 (4 months ago)

I just learned this and I’m in 4th grade

karri ramakrishna (4 months ago)

THIS IS THE SOOOOOOOOOO MUCH INTERSTING VIDEOS

BELIEVE Me Brother (4 months ago)

Am learning calculus from code academy ,its fun and better than my boring teachers who bores me to death ..... BTW nice explanation I understood most of what's said

ngsv raghavendra (4 months ago)

Simply Outstanding!!!!

Hugh Jazz (4 months ago)

INCORRECT: Neither Newton nor Leibniz invented Calculus. It was stolen from the Indians. Just like the Pythagoras Theorem, Fibonacci, etc.

Zhen Cheng (4 months ago)

I still find it difficult to understand, starting from scratch, there are still a few terms which is assumed that the learner understands. It would be great if even words like derivative and integrals are broken down even further. Thank you very much for the video too!

Socratica (4 months ago)

Thanks for your suggestions!! We will definitely follow up with more videos about these specific topics in more detail. LOTS more to come!!
We're so glad you're watching! :D

Chris Jomar (4 months ago)

ihope it doesnt discovered huhu

sue she (5 months ago)

Solve Riemann

sue she (5 months ago)

Discovery or invention

Victor McLean (5 months ago)

Correction geometry came from Ancient Africa aka Egypt

سنا هانى (5 months ago)

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.

Hafiz muhammad Ibrahim jaffar (5 months ago)

This channel deserves more subs

Hafiz muhammad Ibrahim jaffar (5 months ago)

Socratica I do.

Socratica (5 months ago)

Thank you for saying that - you're so kind! We are working hard to grow. Please share our videos - that really helps!

Mahrukh Aslam (5 months ago)

Whos never understand ever 😂

Sajad Ali (5 months ago)

Bhagiashree, a girl of my class come into my mind when I hear about Calculus. She is amazing at Mathematics.
Your videos are very neat and clean Socratica.

Sajad Ali (5 months ago)

haha.. sure.. but I believe she would come read my comment over here. so make it pinned, if you could pls. thanks and have a good day.

Socratica (5 months ago)

Give our best wishes to Bhagiashree! And thank you for your kind words. :D

Man Of Arms (5 months ago)

Calc rocks!

BigV (5 months ago)

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

Best player (5 months ago)

I will never forget this video and the teacher.Thank u a lot

Jonny quest (5 months ago)

Wish I watched this while still in high-school but I will learn maybe I will be of help. Kudos

Jonny quest (5 months ago)

Wish I watched this while still in high-school but I will learn maybe I will be of help. Kudos

Venkatesh babu (5 months ago)

The force of push and pull of matter.

melodie gauthier (5 months ago)

Very very good video!

Saurin S (5 months ago)

very good explanation. thanks..

Safa Ashraf (5 months ago)

This is really awesome..!!

Doug R. (5 months ago)

Actually, Archimedes used a summation technique to find the volume and area of the sphere, cylinder and cone, anticipating the same developments in calculus by 2000 years. His Codex A and C manuscripts were lost, and his Codex B was almost erased and written over by monks. Codex B was re-discovered in 1906 in Istanbul (in the Hagia Sophia Library)and portions were analyzed, translated and published. Archimedes proofs use the same techniques for integration taught today.

Arbaaz mir (5 months ago)

Thanks! it gave me a good insight of calculus.

mike johnson (6 months ago)

Some people are just good at math period & other people suck at it I'm not sure if it's because of the brain not getting it or they simply find it boring, people are not created equal who ever said that is the biggest ass.

Sanjay Shinde (6 months ago)

Excellent. Thank you very much.

Sania Maroof (6 months ago)

whats a function and what do those lines mean in the graph?

Witch Returns (6 months ago)

I understood nothing...

Raimo Kohonen (6 months ago)

Too easy xd

Pain Peace (6 months ago)

I need to re study about calculus..

νεκρός (6 months ago)

I didn’t know Alberto from wwe is math legend.

Vivek Ramanaidoo (6 months ago)

Im just a gcse student and he made me understad calculus thats mad

Justin Epperly (6 months ago)

Excellent intro.

Khagendra Kumar (6 months ago)

Please make more videos

Khagendra Kumar (6 months ago)

Awesome thanks

Hamid safi (6 months ago)

charming...and i have easily understand

Sera K (6 months ago)

Your lectures are so easy to understand. Please post more videos for calculus and vectors.

husam botros (6 months ago)

Actually a new analysis of a set of ancient clay tablets has revealed that ancient astronomers of Babylonia used advanced geometrical methods to calculate the position of Jupiter ie calculus – a conceptual leap that was previously thought to have occurred in 14 th century Europe. Ha ha ha ...u need to update your information m8..

PhoeniX [LynX] (7 months ago)

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

smit shah (7 months ago)

how does he finds the slope

mark fullilove (7 months ago)

I wish you were my calculus teacher.

Otherkin SW (7 months ago)

Thank you

Sandra Hawkins (7 months ago)

Calculus looks really interesting!

Einar Ekeberg (7 months ago)

This is an absolutely fantastic video. Thank you so much

Socratica (7 months ago)

Thank you for watching!! :D

Knower Science (7 months ago)

amazing explanation

madhurima buragohain (7 months ago)

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

Venkatesh babu (8 months ago)

Calculus is add and subtraction up to infinity. Somewhat like circles. And sequences.

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