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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 (662)
## Would you like to comment?

Ray Rocher (3 days ago)

thanks for the education, god helped me feel better about my intelligence, you are a great speaker socratic.

WizaDude (3 days ago)

I'm going to do calculus in a year and I'm interested why students hate it.

vikingslayer34 (8 days ago)

I'm so glad I spent many nights on calculus. I use it all the time in my day to day life. Said no one ever. At least geometry and trig are useful.

Khorne Bezerker (19 days ago)

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

Socratica (19 days ago)

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

Kyle K. (23 days ago)

In short, algebra runs into issues when trying to solve problems dealing with infinity and zero. Essentially, when trying to solve infinitesimals with algebra, you run into paradoxes, such as dividing by zero, a function approaching a point that is too small to analyze, or a function resulting in a solution that goes to infinity, or if a function is impossible to solve algebraically, but you need to still know what it does at a certain point. Mathematicians were puzzled by this for thousands of years, and then came calculus, which resolved these paradoxes. Calculus has the power to do what algebra can't; yet, you often cannot solve calculus without algebra! In fact, in Isaac Newton's 'Principia', he used algebra and geometry as proofs for his calculus. They are important to each other, and go hand in hand. If you need to know what a function is doing at an instantaneous point in time (Differential Calculus), you need an approximation over a combination of numbers, or need to know the area under a curve (Integral Calculus), what a function looks like when it goes towards infinity or gets close to a specific number (Infinite Series), or when you still need to know what a function looks like that's impossible or too complex to graph, plot, or solve (Taylor Series/Approximations), then calculus is what you need. It is incredibly powerful, and without it, modern engineering, space flight, air travel, modern medicine, biology, physics, economics, and computer science would not be possible.

Phuntsog Wangdus (28 days ago)

thank you .. Very interesting and educational video Socratica :)

royal fern (29 days ago)

Where’d you learn that... dope school

K Ayala (1 month ago)

I agree, this was really a great explanation.

PRATIK SAHA (1 month ago)

Very well explanation sir

Jhon Khan (1 month ago)

thanks sir please make more videos on calculus

Ashton9268 (1 month ago)

I'm Amazed I'm So far 16 1/2 years old! I understand it now. And tomorrow's my birthday. Wait until my parents hear the good news.

durgeshkushwaha69 (1 month ago)

What is function in math and how it works in real life

Emana Banana (1 month ago)

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 :)

Alain Smith (1 month ago)

Fuck Mathematics ! But I like your vid

Sakib Dewon (1 month ago)

Fuck this is great

Ashish Garud (1 month ago)

What 🤔 is the difference between CALCULUS and MATHEMATICAL ANALYSIS (real)?🤗

Sun Lun (1 month ago)

Differentiation is used to find the smaller straight lines in a curve by zooming in and integration in simple terms means to add the small lines we've found by using differention , correct me if am wrong.

Sun Lun (1 month ago)

As the saying goes Calculus is the language of God.

Magnetic Allah (1 month ago)

They stole!

Racool9876543210 (1 month ago)

This makes me excited for 10th Grade

moist faucet (1 month ago)

20 years ago there is no internet teaching. i graduate from 4 years college now i know what i went wrong. the teacher is underpaid.

Hussein Mustang (1 month ago)

Translate into Arabic please

Charles Teale, Sr. (1 month ago)

Beautiful presentation!

Mohammad Tauseef (1 month ago)

Wonderful.

dm (2 months ago)

Nebulous

mas bro (2 months ago)

0:30 i dont understand about functions, what is that, why they have to draw curve like 0:30 , and why does have to start like that? what is that curve for? What is it for? What is the history of that curve? Why do we need to learn curve? Anyone who understand this please reference me a link video to understand. Thank you so big much. May god bless us all.

Aman Khatkar (2 months ago)

I’m such a nerd, I’m only in 8th grade and I just thought ’hey I should learn calculus!’ But ur video’s really straightforward thanks!

Socratica (2 months ago)

We're so glad you're curious about math! Thanks so much for watching. Keep us posted about how you get on!

Ranganath Bhupalam (2 months ago)

useful video on this topic.. only the background music disturbs and distracts.

blake (2 months ago)

I honestly wasn't able to understand calculus for 2 years but now i got it 2 DAYS BEFORE MY FINALS

ionisator idk (2 months ago)

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

Justin9067 (2 months ago)

6:53 looks like a zit

Ganapati Hegde (2 months ago)

Awesome explanation. I wish I had teachers like you.

Emad Rahi (3 months ago)

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

king jufu (3 months 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 (3 months ago)

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

MLG Player (3 months ago)

Ah the thing i wonte study i hat math

Sanam Khan (3 months ago)

Oh I just completed 10k likes in 10 October 2018

Md Bahar (3 months ago)

Great teacher, God bless you dear.

Research (3 months ago)

I wish I never did drugs!

GrumpyOldMan (3 months ago)

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

qualquan (4 months 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 (4 months ago)

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

Jeremy Metcalf (4 months ago)

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

Veronica Worthen (4 months ago)

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

stonent (4 months 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 (4 months ago)

It was a great explanation. Thanks

John Batchler (4 months ago)

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

John Batchler (4 months 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 (4 months ago)

Good Work !!!

Mantej Singh Dhanjal (4 months ago)

What are the real world examples of Calculus?

anjali Dass (4 months ago)

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

Prithvi Sundar (4 months ago)

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

Namah Shrestha (4 months ago)

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

Ayush Singh (4 months ago)

i am in 9

subith sjohn (4 months ago)

This is too complicated for me but are really good

Alexander Kenny Wen (5 months ago)

Quality Content!

J (5 months ago)

I wish you were my calculus professor

Ramesh Reddy (5 months ago)

Sir do more videos on calculas we are waiting

Derec Wilsom (5 months ago)

Very nice intro

Blue Hamster of Redemption (5 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 (5 months ago)

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

Stefos (5 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 (5 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 (5 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 (5 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 (5 months ago)

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

johnpro2 (5 months ago)

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

NIRMALYA SENGUPTA (5 months ago)

Excellent video!!!

sreereka baskaran (5 months ago)

You are great,thank you sir

Satish Pandu (6 months ago)

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

Jonathan Haddad (6 months ago)

congrats you just taught a 15 year old Calculus

Souvik Dey (6 months ago)

Super sir..love from India 🇮🇳🇮🇳🇮🇳

Serin S (6 months ago)

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

darkdoctor2017 (6 months ago)

They discovered or they invented ?

WebDev (6 months ago)

Thank you very much!

REGIL TUBE (6 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 (6 months ago)

Fantastic

shamusfarmer (6 months ago)

Nope.

Sakshat Karandikar (7 months ago)

Ha ha calculus was invented in india

KRIPA SHANKAR SHUKLA (7 months ago)

Totally amazing explanation!! THANKS A LOTTTTTTTTTTTTTTT!!

Chelle Weatherspoon (7 months ago)

Wow! This was really helpful.

Arpita Sarkar (7 months ago)

NC explained

HIMESH VIEWS (7 months ago)

Which editing software please tell me sir

Mycroft Holmes (7 months ago)

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

Arjekay (7 months ago)

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

GGGames 101 (7 months ago)

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

HARI SHANKAR (7 months ago)

THIS IS THE SOOOOOOOOOO MUCH INTERSTING VIDEOS

Helping Students (17 days ago)

You are right

BELIEVE Me Brother (7 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 (7 months ago)

Simply Outstanding!!!!

Hugh Jazz (7 months ago)

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

Z C (7 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 (7 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 (8 months ago)

ihope it doesnt discovered huhu

sue she (8 months ago)

Solve Riemann

sue she (8 months ago)

Discovery or invention

Victor McLean (8 months ago)

Correction geometry came from Ancient Africa aka Egypt

سنا هانى (8 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 (8 months ago)

This channel deserves more subs

Hafiz muhammad Ibrahim jaffar (8 months ago)

Socratica I do.

Socratica (8 months ago)

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

Sajad Ali (8 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 (8 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 (8 months ago)

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

Man Of Arms (8 months ago)

Calc rocks!

BigV (8 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 (8 months ago)

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

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