Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007
ฝัง
- เผยแพร่เมื่อ 16 มิ.ย. 2024
- Lecture 01: Derivatives, slope, velocity, rate of change
*Note: this video was revised, raising the audio levels.
View the complete course at: ocw.mit.edu/18-01F06
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
+Osman ÇALIŞIR All the lecture notes, exams with solutions and assignments are available on the MIT OpenCourseWare site at: ocw.mit.edu/18-01F06
"notes" are typically when students copy what is written on the board, so then those ARE all the notes.
it's a triangle, resembles a trialgle
Is video for 18.014 available?
Thanks to all at MIT.
@Marcelo Esteban Mauricio Δ is actually a greek letter and it is used to express diferentiation from the greek word( Διαφοροποίηση ), because its the first letter of the word
Lecture 1: Rate of Change
Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review
Thank you!
I really needed that as i am preparing for entrance exam
Helps me a lot.
Thank you!
Thank you
Anyone else most thrilled about the quality of their chalkboards?
As well as by the size of the chalk chunks :)
Love chalk boards...
OMG YES!!!!! Firstly the chalks are so bright and seem effortless, I don't even think there's any dust. And secondly they wipe off even faster that whiteboard markers! It's crazy! I can almost imagine the feel of those chalks rubbing against the boards.
Chalkboards make me happy.
@Tidder T Yeah I guess Hagorama !
100 students in a class. each pay 50USD a day aprox for university. perhaps 25USD for this lecture alone. (2500USD total!)
And we get it for free!
This really helps those without opportunities to learn and advance.
It really does! I'm actually use these courses to learn everything before I go back to school, so I can get the high grades, and make school easier when I do go back.
is there a point to boast?
Not only are we watching it for free, but we have the ability to rewatch this how many times we want, unlike the students who are present in the lecture.
They get the degree though. That's what they're paying for.
they get the degree and can apply job anywhere they want
This comment section sure has a lot of egos. Math brainiacs feeling the need to show off their mad skillz: humility might do you some good. It's fantastic that this stuff is incredibly easy for you - it isn't for everyone, and proclaiming your genius to the world serves no one, it only comes off as arrogant.
If this is below your level - great, go to some higher level videos. In the meantime, show some respect for MIT and appreciation for their work in making good education open to everyone, and some consideration for your fellow students who may have more trouble with this stuff.
+Tinydude10
This is truly fascinating.
Further ago, the physically superior human would find no fault in demonstrating his own superiority, whereby others would submit in his presence. But today, we do not see the same consequence in the intellectual realm.
+ Tinydude10
For reference, I submit quickly to my intellectual superiors, that's how you learn, and that's how you expose fakes. In so doing, you're relearning everything through them, and this will reveal what they truly know and what they don't, to distinguish between a fact regurgitator and a true mathematician.
And of course, that's how you learn. In BJJ, white belts can learn from blue belts, apparently not the case in maths for most people.
S. A. C. L. holy FUCK you are cringeworthy
S. A. C. L. Professor s don't go around bragging lol
Shut the fuck, mate. Get some self respect.
I'm very grateful to MIT for providing all of this for free. Big thanks from Russia!
Kerk32 same
R U SERIOUS ME TOO
Big thanks from China
А каких лекций в России Вам не хватало? Сразу скажу, что не стремлюсь этим вопросом принизить лекции от МИТа, просто любопытно.
One more big thanks from China.
I'm a chemical engg. student from India ..i watch mit videos regularly .. it helps me a lot.. sir.. your teaching style is awesome .. thanking you all.. for sharing such videos ...
Are you bengali ??
Jai Shree Ram
we can share the idea if you feel like. cooljay1080@gmail.com
@@alhadbhagwat6142
Kyu? Kaise? Kaha? Kab?
@@vijaysolanki9801 s1mp
The level of the calculus might be low, but he is explaining the proof and intuition in very clear, insightful ways that you don't normally get from a high school teacher. Well worth watching. Thank you MIT!
ok boomer
@@gamerboyss5310 ok fortnite boy
@@gamerboyss5310 why do people like you come here to infiltrate comment section, you don't even know him and if he is elder then please show some respect and help make this a better place for everyone.
th-cam.com/video/FffvCM0C3x8/w-d-xo.html
Well, what is this exactly? this is definitly not what they teach to normal MIT students. You wont expect such things being taught to one of the top students from each country , many of which are medalists in International math olympiad
we can get free lecture from MIT?? WOW!!!!
i never know that youtube have video like this.
good.
nowdays the question is which type of videos youtube doesn't have
@@atomicity7452How do I make nuke
Thank you MIT. I'm a chemical engineer with over 3 years experience in the industry. Just recently I needed to go back and relearn basis of calculus. This was a great refresher
The voice clarity is very clear . Awesome work by MIT OCW.
Thank you so much to professor Jerison and the MIT team for creating this whole course. I'm starting my journey in Calculus and it is way easier and more appealing because of you.
I really like that the instructors at MIT spend the time to write the topic on the board which reinforces the point of their discussion. And they all have good penmanship which allows the student to concentrate on what he is saying, not trying to interpret the writing. I also like they're using blackboards and chalk which show up nicely in the videos. When my school changed to whiteboards there were times when reflections obscured the writing and some of those markers had a distracting smell.
The fact that anyone anywhere can learn this is revolutionary, I think
Some impoverished Einstein now has a golden opportunity
I don't think I will ever get an admission from MIT :) but being able to listen to lectures from my dream school online for free is truly awesome! Thank you for these wonderful lectures.
♥
Yeah
I hope you get an admission from MIT :))
I am from the Dominican Republic ,
Thank you very much to MIT Open courses.
we are using yours Lectures at the rural area of Barahona city wich is at the South area from Santo Domingo.
Thank you very very much.
God Bless all of you.!!!!
Yes! Most charismatic calculus lecturer I've seen on youtube. I'm biologist and enjoy improve my math skills in my free time. Many thanks from Russia. I'm very grateful. .
4:51 geometric interpretation of differentiation
12:00 steps in computing slopes
21:50 check for the plausibility of computed slopes
25:30 the hardness in solving a problem involving calculus
33:50 use symmetry as a shortcut
37:00 the hardest part of calculus, the resolving of variable names
a set of free lectures from one of the top Schools in the world.(especially the highest level of mathematics) God bless TH-cam.
It’s not the highest level of mathematics
@@David_F97 calculus is quite an advanced thing though, but there are tougher branches in maths
youtube didn't really give us all these materials, MIT did.
Máté Szabó-Galiba god bless both MIT and TH-cam
@@roc6596 applying calculus in physics: am i joke to you?
41:00, (y=1/x)
Area of the triangle
2(x)(y)=
(substitute the original function (y=1/x) into the area of the triangle equation he arrived at and you get.
2(x)(1/x)=2
Omg thank you!! I was having a hard time with this
Really thanks on that, it was only magic until you clarified it, thanks!
Ive always been interested in quantum mechanics but to get there you need to start from the bottom. excited to start my journey!
Good luck! (From the future)
How's that going? It's great that you've embarked on this journey. I started it myself a few years ago and now I've finished the first QM course MIT has on youtube. I could tell you what courses to watch if you want.
@@santiagoarce5672 hi, i know i'm not op but i'm intersted in qm as well, would you mind telling me what courses you looked at?
@@vin2164 for math, I learned single variable calculus (18.01), then multi variable calculus (18.02), then differential equations (18.03), and finally linear algebra (18.06).
In terms of physics I did basic mechanics (8.01), then basic electricity and magnetism (8.02)and finally vibrations and waves (8.03).
After all this is when I did QM. There’s 8.04 and 8.05 on TH-cam as well so it’s definitely enough to satisfy a starting curiosity in QM.
I included the course numbers these courses are given at MIT, so you can look for them on TH-cam.
Good luck!
@@santiagoarce5672 Thanks man! I also wanted to learn QM. This will definitely help.
The Geometric interpretation of the derivative is fantastic. Gives you a clear grasp of the concept before adding any kind of obscure computation. Great work. Thank you Professor Jerison
I really want to thank MIT OCW fore the opportunity to really learn calculus, and even better, from one of the best places in the world. We don't have this kind of teatching here in Brazil, not anywhere near this. I'm very thankful for you opening this class to everyone.
Excellent job . I've never seen such an amazing calculus professor. Thanku so much for this wonderful series.
i cant thank enough. this really help us a lot where we dont get proper teaching. Thank you so much for sharing the videos for free. I wish every famous university were doing that.
I like how people in the comments section are mulling over the Professor's treatment of the material in this course, completely forgetting the fact that courses like these will usually have textbooks associated with them to augment learning and the professor's job is NOT to regurgitate things that can be found in a textbook but to focus on the key concepts required in problem solving.
It amazes me that some people feel that there's a need to do 10 whiteboards worth of derivations in a 50 minute course when the focus should ALWAYS be on the concepts, with the professor encouraging students to look up the derivation or the individual proofs. It's good that the professor managed to do the derivation at the end, cos it just reinforces the concepts and also provides a general methodological framework which students can then use to solve general problems.
the website stated that there's no book accompanied to this course, don't just think it's a good lecture cause it's from MIT. The lecture is disappointing.
@@fisherli7187 I feel like if you’re going to not have a book, then your lectures better be pretty amazing, with extra resources for learning that aren’t bought books.
The other thing…half of math lectures (probably more) always lack some crucial historical context. Why was this made? Why did it matter? And the problems are so abstracted away that it loses some of its magic, just turning into esoteric stuff that’s solely important in esoteric isolation.
And, I’m NGL…I kind of want some sort of strong personality from my math professor. I had at least two of those, and it made everything way smoother and better.
I just don’t see a lot of enthusiasm from this guy.
@@bigbluebuttonman1137it's the matter of level of students too.
Omg I just discovered this channel and I didn’t have idea that TH-cam have this excellent content. It remember me when I was in college and dreaming about being at MIT
¡Gracias por subir este tipo de contenido!
im a CSE student from india and litrally These videos are proving that Why MIT is best in the world....
One of the many things I like about this professor: "Let me tell you BRIEFLY what's in store." Three minute intro, not twenty minutes of child psychotherapy at the start of the course. 15 minutes in and he's explained the derivative.
Big thanks to help me pick up my lost memory of calculus, and ease my scary on this subject. math is beautiful.
I hope everyone realizes this is the beginning of calculus. I'am a freshman in high school watching out of pure interest. If your farther ahead of this; move along and don't comment on "how easy this is"
This man is amazing. I used to only be able to compute derivatives and limits, but this man made me understand the why and how of it as well.
I wish I had this prof for Calc... So much better at explaining what he's doing than the one I had
He is a very good teacher! I'm taking a calculus course now and using this for review. He has received awards for his teaching. Thank you MIT for providing this for free!!!! It's remarkable and free teaching at this level is changing the world!
Thank you all in MIT for sharing this class with the world. I like it, a lot. Mathematics rock!
Thank you to whoever did the closed captioning (subtitles) on this - tedious work, but very appreciated.
I love these lectures!!! Now I'll be able to get ahead in my highschool math!!
THANK YOU MIT!!!!!
That's cool
Me too!! I really want to be able to take MVC by senior year
If majority of people are interested in science and math like they do in music and cinema, it would literally push civilization to the next level.
I am truly impressed his lecture.... I have learned about derivatives so many times but I didn't really realize why formular be made like that way.. or act like that way. AMAZING
In Russia we learn this in 10th grade. In America they also learn this in 10/11 grade however this is just an review + some new stuff. This course lasts for only 1 semester. In school it takes you a year, while this is ONE SEMESTER.
US still has and will have the best engineers in the world because they think creatively, and not just learn everything in the world. They apply their skills instead of inventing new. And no offense to anyone not in US, every country has amazing universities.
But I think most of the guys that are working in Silicon valley are asians.
In Brazil we learn calculus just in sciences college/university
@@raghav9o9 you are thinking right
I love the boards and the chalks so much that I can fly there and solve a tangent line problem on those boards with those lovely chalks. What a chalk to write with, and what a board to write on.
@@KB-ur4nk Slope (f'(x0)) is not a line. It is a property of the line i.e. it is a value. f'(x) is a curve (represented by -1/x^2) obtained by plotting all these values(slopes) for different values of x i.e x0, x1, x2.............
I love the sound of chalk on a chalkboard.. he has great handwriting
I first saw this lecture some 10 years ago. It a fantastic lecturer MIT has in David Jerison. It is a marvelous course in my view. Thanks to MIT and David Jerison for this and other lectures I 😊😊😊have followed. I can only recommend all interested in this area to follow MIT courses.
Brgds John Sørensen, Denmark
I'm a second year calculus student, and I find these videos very helpful. thank you MIT, for making these awesome videos.
Wow you have graduated, married yet?
@@78anuragtheir music playlist includes a song that’s 8 months old. So they’re at least alive as of 8 months ago
Mit is doing a phenomenal job by uploading these
This guy can teach. He is not pretentious, and is not afraid to explain the algebra behind the calculations. I remember my freshman calculus course. If you forgot any of the algebra basics there was a lot of uncomfortable silence.
Listening to cinematic musics while watching the lecture makes me feel like I'm in a top secret project and I'm the most important agent
which song?
Very impressive and helpful specially for the people who can't afford to study but still want to learn in life.
The video on my recommendation .And I cant stop watching . One of my dream university when I was in secondary school.
It's been over 10 years since I first learned this in high school. Now I think I finally understand the formula for the derivative after this guy lectured for 20 minutes.
Thanks Prof. David Jerison and off course MIT and American society for this amazing science dissemination!!! The American society formed by the founding fathers is an example of freedom for humanity... thank you.. I love you..
The only thing I can say is these lessons are WONDERFUL thanks a lot for your efforts as soon as I finish the entire playlist I will leave my comment under the last video I'M so glad to be made follow the lessons without being in this class
when you gave these lectures I was just 3 years old and now I'm improving my Maths knowledge by myself because I love Maths a lot..
Greetings from TÜRKİYE✍✍😍😍
if only I had known about this open courseware thing when I took calculus the first time, or even the second! Thanks, MIT, for sharing knowledge. Kudos to this professor, for shedding light on this monster class.
So good for doing this, even it's ordinary. Very good self-study material.
very good explanations..
description doesn't enlist his name?
i am very thankful to MIT for putting these kind of videos in public domain.
Derivatives are cool and all.. but have you ever tried a stuff crust pizza?
well its a circle wouldn't it have all possible gradients?
Better gradients. Better pizza. Papa Calculus.
Well, I would assume it's THICC and CHEEZY.
It’s in-gradients are amazing!
@@trekker146 LMAO
These students that were attending this class were excellent students, but the way the teacher/professor taught it
step by step slowly and slowly is really a beautiful thing. Really appreciate that thank you professor.
these lectures are excellent for indian students who learnt entire caclulus by byhearting formulas and now need to understand how everything works
I love the teacher's handwriting!
this is awesome, i feel like a student in the class :)
The BIGGEST W to MIt for actually making high quality educational content free for people. I wanna learn calculus over the summer and this is great!!! Thanks a lot!
I’m taking calc AB right now as a senior in high school and so far I know all this stuff but I plan on watching all the vids until I can understand it through these and then go over it again in class to make me double prepared this year, thank you so much MIT for this opportunity.
i thought calculus starts with sets and functions or am I missing something?
in highschool it starts with like some review of functions and function properties, then gets into limits
Went to the later MIT lectures for this course about 900,000 people have watched this vid only about 50,000 people actually got all the way to the end. There's a huge drop right after he finishes what most colleges consider calc 1.
If I had to hazard a guess, people probably get frustrated once they get to all the technique memorization notorious to Calc 2. Which is a bit sad because Calc gets cool AF once you've finished said grind.
If you are wondering he is using the slope-point formula in minute 30:38.
I would also appreciate if someone can explain to me why he can use O(x²) in minute 47:30 to describe values with bigger exponents then 2 like x³,x⁴ and higher.
Because the other terms would approach 0 when delta x approaches 0, there needs to be nx^n-1 because there’s a 1/delta x
Thank you MIT and my dear sir. I need calculus to study MIT physics. So I started my journey today. I could understand the whole lesson. Thank you again.
This professor is detailed in his calculations and explains why things work the way they do
I can't thank MIT enough.
I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.
What previous math categories should I learn to continue on with calculus?
+Ahbrah The prerequisites are high school algebra and trigonometry. See other resources like the Kahn Academy for coverage of those concepts.
Khan* Academy. Sorry couldn't help it lol
Algebra and trigonometry. Sine cosine and tangent basics taught in high school algebra, and trig. Without these, this all seems like a bunch of random Greek characters and woo. I agree, Khan Academy is a good resource. Also, a few cheap used school text books from amazon would do the job...and would also provide a good structure for the prerequisites that this course assumes are present. In fact, I would recommend the book route rather than the Khan route, and then use Khan as a reinforcement to test your knowledge, as the website includes practice tests, but does not provide the linear progression you need.
You need coordinate geometery as prereq . Download cheat sheet from google understand them and solve atleast 8 problems of each type . Come to this very first lec. of calculus again u will be able to unberstand most of the portion .
Okay what about limits? :D
THANK YOU MIT FOR THIS VALUABLE LECTURE !!
For a very first time in my life, I understand calculus. Thank you so much
🙏
What is wrong with most of you commentators? If you are too smart or too good for these lectures then go somewhere more challenging. No need to show off how smart you are by stating how simple the work is for you.
Casey Stack youtube "geniuses"
+Casey Stack insecurity... which is why they're bragging on the internet, for the most part.
+Casey Stack also, the purpose of calculus is not in it's varying levels of difficulty, but in it's application.....which can yield more than the creative mind could conjure. math is essentially a tool used for creation, and not a d**k measuring contest.
why do you even read the comments, its how people express what they understand,
I’m doing this in my high school class and I don’t understand fuck. I’m like the only sophomore in that class with a bunch of seniors. It sucks.
Generally people from India, specially Bihar think that they are very smart in mathematics but that's of type "Rattafication" a/c my experience
Here's the actual mathematics !!!
Literally Loved this lecture, wish to complete whole calculus part from here, not for any entrance but just to make my understanding to next level!
Thanks MIT :)
Thatswhy it is MIT not IIT!
Even I cleared JEE Adv questions by rattafication because we were taught to do so and I am from Bihar
@@pepewr You are Right!
I also belong to Bihar
i simply enjoy watching and listening to this.
这老师真好， 看了这个课之前，我以为我遇见的是好老师。
我遇见的数学老师，从来没解释过，坐标系里，其实是很多个变量，而且重复使用了x 和 y 来表示不同的东西。 而这一点是非常重要的，也是复杂的根源。
I enjoyed this professor's lecture. It helped me conceptualize a new idea.
my brain is on fire!
Lol this comment made me chuckle. Thanks
Did your hair survive the extreme heat? Is that why people have evolved to go hairless on their heads for better cooling? And, how did hairless heads apply to physics?
Currently a sophomore in high school. I've heard a lot about calculus over the years and about just how powerful and beautiful it is. About 20 minutes in is when that rang so true for me.
i feel honored to be able to listen to a MIT, math professor. I am trying to teach myself calculus this summer but his lecture is kinda advanced for me at this moment. lol.
Perfect revision after almost 30 years ! thank you .
inspiring, sir
44:15
Thank you very much to MIT and Prof. Jerison for this great public service. Are the backwards question marks he draws on the board something peculiar to MIT?
We never could know what we learn in TH-cam or Bilibili. Thanks MIT , Peking University and other universities those could really bring knowledge to me.
Do these courses pretty much teach you the same thing that a high school AP Calculus AB class would?
yes
Hero Man
What about AP Calculus BC?
I know it covers more material. Integration by parts. Parametric Equations. Taylor Series.
That is on here, but I HIGHLY recommend supplementing this class with a more complete textbook. They are covered, but their work on Series is a little deficient. I hope this is still useful to you, 6 months later!
They do not waste their time, they learn only required things.
I have a question to all the people talking about "how bad american education is", why does everyone from around the world want to come to MIT? Why are MIT graduates so succesfull?
America's Elementary, Middle and High school level of education is deplorable relative to schools in other countries. Their higher level of education is phenomenal. Schools like MIT, Harvard, Stanford and Princeton are synonymous to great success all over the world (as you said). I'm currently studying at Cambridge and I'm watching this lecture :P no shame in that because it IS VERY GOOD. Sadly that standard can really only be met by students who have had a much more rigorous studies prior to entering their secondary level of education. People from other countries (as you said) will flock to your higher level institutions because they are more likely to meet the standard.
+xEAx1x Not true, if you adjust for demographics, whites in America are average by western European standards. North East Asians in the US perform similarly to Northeast Asians in Northeast Asia and people from third world countries probably do better in the US than in the country of their ancestry. It only looks bad if you assume that all peoples are equally educable and have the same innate ability. An assumption which I see no reason to make, and hence the need to control for ethnicity.
The Eternal Hermit is this knowledge from your numerous years spent studying anthropology. Lmao, never thought I'd see such Idiocracy in one of MITs videos, usually stupid people don't come here
The education when terribly because of the civil war and world wars
thank you Dr. am from kenya, university of nairobi doing econ, this is very helpful
This man's jugular is noticeably extended indicating a high degree of self-induced stress. Dangerous work well performed.
Today I have statrted this course. This is really awesome. I just want to know which book I should follow for this course?
The textbook listed in the syllabus is: Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, October 1, 1996. ISBN: 9780070576421. For more info, see: ocw.mit.edu/18-01F06. Best wishes on your studies!
Thanks mit
@@mitocw I love MIT physics and it's fascinating
This guy is great. I studied engineering at a university less prestigious than MIT, and I remember professors refusing to explain their algebra steps. They were like "you should know this already".
I need to finish this, rewatch, and then continue (all of it, besides the physics part)
Everything Just Makes Sense
@stiglaa
X value - any value on a graph's horizontal axis
Y value - any value on a graph's vertical axis
slope - the value which is the change of x and y values between two points
tangent line - the slope of a curve at any given single point.
In this video he estimated the tangent line by looking at how the graph curved in that area. (Geom. Interp.)
Wow they start by differentiating e^(arctangent(x))d/d. My community college we start with xd/dx
28:10 - I've done an interactive graph of this exercise at: www.desmos.com/calculator/lfc29dwtt6
Finally a professor who gets straight to the material. No wasting half a lecture on philosophical gasbagging.
In my highschool book, it proved the factoring of x to the n - y to then n with polynomials and horner. You devide that by x-y such that the remainder is 0 and if you do the horner, the factored identity comes out.
Is there a way for senior citizens to audit these classes in person? This would be a dream retirement.
Why do College Profs use such Large chalk???
+Jim White Chalk does tend to wear down over time...you want to make sure you have enough to cover all the concepts covered in the lecture.
+Jim White Sorry for the late reply! Sometimes we request instructors use the jumbo chalk (aka railroad chalk) for better visibility when recording video lectures. Some instructors use it on their own for the bigger classrooms to ensure that everyone can see the chalk on the boards.
+MIT OpenCourseWare So that's how it's called. Awesome!
Because they can.
It’s not the size of the chalk that matters, it’s how you use it
love seeing teachers look at notes
Thank you from Colombia, it is pretty useful!
Man I love chalkboards n the sound the make :D