We are spoiled. I am going back to grad school so I am brushing up on Calculus and let me say the second time around has been cake (in terms of learning and accessibility of information). I can't believe the difference in the level of exposure to information between then (late 90s) and now. Back when I was taking Calculus I never thought that someday I would be listening to and watching Calculus lectures from a professor at MIT in my house or on a walk. What a wonderful time to learn. This program at MIT is truly exceptional. Even my teens are watching along and getting exposure. Strang is perfect.
+Casey Ryan Agree, he's amazing, especially for someone like me who knew nothing about Calculus. He coaxes you along, something like teaching an animal to trust.
..Dr Strang is enthralling. I would be obscenely jealous of your having for a professor except for two reasons: He got his doctorate at my alma mater, UCLA, and my calculus teacher at UCLA was Dr Matthew Brodsky, an MIT graduate! You guys do good work.
I GUESS THE NUMBER OF GREAT MATHEMATICIANS IN THE WORLD SHOULD TAKE A LEAP-STEP BECAUSE OF INCREASED ACCESS AND EXPOSURE TO GREAT 'LEARNING MATERIAL' -->MATHLAND
This is the reason why MIT is a great school to go to. They teach conceptual understanding and ideas instead of a step by step method to solving an equation. It's annoying that teachers dumb down calculus simply as a means to prepare for a test or an exam. This is why we're only as strong as our weakest link. Teachers shouldn't be judged by their flunk rates. Those who want to succeed, will.
We're such a lucky generation, i'd think of only 20 years back how it would be hard to reach such understanding. Big thanks for Prof. Strang for how unique way for teaching the meaning and not the steps !!!!!!!!! And For MIT open courseWare: you are making the world better :)
Everything makes Sense. Literally Goosebumps moment. Thanks a ton. Free education empowers you exceedingly. Thanks to MIT and the sponsor. You have impacted many lives, I believe.
I remember this stuff at high school but was completely boring then. I love it now. Feels like Im peering through a keyhole at the secrets of the cosmos.
Thank you Professor Strang for this amazing series on Calculus. I'm a high school student and this was extremely helpful. You've made it so much more easier for people all over the world to gain access to invaluable knowledge through your lectures and God bless you for this!
I wish I had come across this series of lectures when (or prior to) starting my calculus one course (I'm almost 31 and only beginning school now, after dropping out [or being kicked out], for all intents and purposes, at age 15)... I was able to understand the "big ideas", so to speak, of what I learned, but they really only clicked after the course ended and I had time to step back and actually play with the ideas. The class was so focused on technical details that it was difficult to see the beauty and cleverness (and actual fundamentally understand) of what is going on. Of course my algebra skills are, and always have been, dusty; albeit I've been able to ace the GED and placement tests, it was always due more to memorization and brute force than intuitive understanding. These are the same problems I encountered growing up in school; there was rarely a teacher that knew how, or cared to, teach things in a way that would enable you to appreciate what you were actually doing. Not only is this why people tend to be uninterested in math (and technical things) but it is why the teachers and students are ineffective. Our education system needs some serious re-evaluation. Thanks for these lectures Professor Strang.
Thank you Dr.Gilbert and to the MIT people behind this initiative. This is a perfect example of how much difference an excellent teacher can bring about in the learning process and make seemingly difficult concepts graspable to anyone at all. I have started appreciating calculus so much more.
This is priceless! Thank you MIT and Professor Strang for making this available to everyone. I took calculus at college but could never really understand the basics in such a clear way. I think the best way for us to return the favor is to share all the things that we know, so people that can´t pay a top-college tuition can access to top quality material.
Not enough time and effort is invested in instilling this “big picture” idea-based understanding. Seems to occur mostly in higher college courses. Great teacher. Wish there were more like him.
Man, if only I looked for MIT open courses before. I would have brushed up on these concepts 5 years ago. Still not late to learn from great professors.
I couldnt believe I was actually enjoying these lectures, and have found myself drawn back into maths "for the fun of it" 10years after leaving college! Thanks dr s. Amazing man.
Just what the doctor ordered. I wanted to delve into my old textbooks, but had lost a lot of the ideas that made sense of them. This was the perfect refresher to get started. Thank you very much!
Thie professor has a good way of explaning how this works , in the past i studies electronics and learnet this math but never got the feeling that i have after watchting this video , it's very good explained.
Thank God I finally got an explanation as to why derivatives work. I missed a day of math for a wrestling tournament and never got it explained to me, and now that year and a half long itch has been starched.
Thanks Professor Strang! I was looking at practice BC Calc problems and after watching your video, it demonstrates that Calculus is not just some strange abstract voodoo math with alien derivatives and integrals but just taking algebra to the next level and understandable!
slope and speed are the first prime or the first derivative of a given function. If the car is travelling at y=mx+b, then by applying the power rule of a derivative then it's speed is m. In this discussion, Professor Strang clearly and wonderfully shown to us the concept/idea behind the power rule more than just as nX^n-1. Thank you Professor Gilbert Strang.
thanks to Mr. Strang. Poor people from developing countries now have the chance to have top level education. People like Mr. Strang should be given some kind of noble peace prize not to politicians who pretend to be peaceful but are actually war mongers. God blees Mr Strang wish there were more good people like you.
I am from a developing country. Since the day I knew the MIT existed I wanted to go there, but I knew It was too difficult. Just 1% in my country make it to go to college. TO GO...and less (much less) than those get a degree. I entered college and was doing great, but after finalizing the secong year I had to quit because I got sick and didnt have enough money. This is like a dream come true in a sense to me. I can attend MIT!!!
I love the way this course is presented. I hope I can find more of these videos to cover all of the topics. It is review for me but my first course was not fun to learn.
at 3:00 AM in the morning / night .... feeling lucky , this course is an Eye opener .. having my Eureka moments, Awed by Prof. Gilbert Strang's deep connection with the Mathematics that as if he also re-discovers it every time he lectures ... it is beautiful ....
His manners are charming and his attempt to make things really clear from the very beginning quite successful. 14:30: the formula of average change is wrong because he writes (Delta x) ^2 over Delta x instead of Delta x^2 over Delta x; he goes further to equate the quotient with Delta x, which is 1 instead of the 3 he had previously computed.
+Navin Sawalani No, sorry, look at the screen. He writes 'average', not 'instantaneous'. Capital delta notation is used for computing the average rate of change. It should be: 'the change in x^2', i.e. 'Delta(x^2)', not '(Delta x)^2', which means 'the square of the change in x'.
***** He is speaking of the average rate of change of the function f(x) = x^2. This is Delta(x^2) / Delta (x). Sorry if I can't understand you. But (Delta x) ^2 / Delta x is just Delta x, of course, and it is simply the change in x, not a rate of change..Thanks, anyway.
Recommend watching at 1.5X speed if you are following along well. It helps save time while getting the full information. Feel free to rewind or pause if you need a minute to process something.
sir you are truly amazing :) my teachers have neglected the understanding of mathematics but it all makes sense now. because of you now i actually understand :)
@18:12-18:16, "This is all algebra now. Calculus is going to come in a moment, but not yet' The professor carrying the audience into thrilling scene! Wow, wonderful cognition shift!
I have a question. So, we have the function y = x² The slope of this function when x = 1 is 2 (because the derivative is y = 2x). And the slope when x = 3 is 6? (We simlly insert value of x in our derivative function?)
Thank you so much Dr. Strang! I love your teaching style and methods... and I appreciate all the hard work of your videos... It has helped me review my calculus skills for Econometrics and Econ Mathematics this semester in grad school. I wish that I could have had you as my original calculus professor! :D You are awesome! :D
He reminds me of my old physics teacher whom (I have no idea if I just used whom correctly hah) I had in, oh well, 7th grade or so, and he was the one introducing us to atoms and molecules and all that stuff. Everyone thought he was boring and dull, but I think he was a nice guy - just like this guy (: Respect for that old man. And thanks for a great lesson! I've always dreamt of how it was to be at MIT or Harvard or Oxford or anything like that!
After watching this video for 30 seconds, I understand more than what my teachers ever made me understand. I'm now actually quite angry at how bad teachers I have had. My suspicion is that they did not really understand it, an yet tried to learn others. Not the best idea. Big thanks for these videos:)
You have a vastly superior culture, this school is one of America's best and only a few very smart people go there, and have to pay 100,000$ a year to be there!
function graph slope at different points first increases and then decreaces at peak point and function derivative give cosin x function whose graph show increase and decreasce in the value of slope of sin function on graph
Gracias profesor por su enseñanza y gracias a mitopencourseware por su apoyo a la divulgacion del conocimiento para todos los habitantes de nuestro planeta Tierra. El conocimiento de las matematicas nos ayuda a proteger nuestro planeta y a dar bienestar a la gente.
21:10 I get that 2x + ∆x = 2x if ∆x is very nearly zero. However, how was it possible to get to 2x + ∆x in the first place if ∆x = 0? You'd be dividing by zero, no? I'd be grateful if anybody could explain this.
It is not that Delta x is almost equal to 0 but that we, in computig the derivative of x^2, are interested in the limit of 2x+Delta x when Delta x tends to 0. And this is obviously 2x. Delta x is never 0, it only tends to.
It's impossible to explain. It's a lie. It's a hack. It's nonsense. You know it's wrong but since our 'teachers' told us we have to religiously follow along.
It can't be x^2, you are only dealing with one side of the slope, since you are only dealing with one side of the slope it is y=mx+c not y=x^2. x doesn't go on the y-axis. x only goes on the x-axis therefore you can not subtract it believing it is going up the y axis. It should be minus y? How are you evaluating x up the y-axis?
y=f(x) and obviously if x changes a little then y too will change and mathematically we can say y+dy= f(x+dx) which leads to dy= f(x+dx)-y or f(x+dx)-f(x) and soon we can say dy/dx= {f(x+dx)-f(x)}/dx. The only job for the transition for calculus is to apply limits ... and there is the problem.
Mr. Strang is a Professor of Mathematics. He has spent a great deal of effort and time working toward a PhD; meaning he's earned the title of, "Dr. Strang". It might seem petty to address him with the proper title, but it's kind of a big deal.
Its funny how i may be the only business student who has to go through calculus, and not having this in high school just makes it even more harder for me to grasp the basic concepts :(
I like explaining it like this if f(x) = x^2 then f(10)=100 and f(11)=121 so its up +21 this thing caller a "derivative" lets us estimate the change d/dx f(x) = 2x which we also write as f'(x) now f'(x) evaluated at 10 is f'(10) = 20 which is pretty close to 21 (5% err) it works better with bigger numbers f(100) = 10000 f(101) = 10201 so its up +201 f'(100) = 200 which is pretty close to 201 (0.5% err) and it also works better with smaller changes f(10) = 100 f(10.1)= 102.01 so its up +2.01 f'(10) = 20 so it should go up 20 for each unit of input increase so 20 * 0.1 = 2 which is pretty close to 2.01 if f(x) = x^3 .......
![[BONUS] Quand le patron du PSG impose sa loi aux autres présidents de club (Version longue)](http://i.ytimg.com/vi/xjZeo7FIWQg/mqdefault.jpg)
We are spoiled. I am going back to grad school so I am brushing up on Calculus and let me say the second time around has been cake (in terms of learning and accessibility of information). I can't believe the difference in the level of exposure to information between then (late 90s) and now.
Back when I was taking Calculus I never thought that someday I would be listening to and watching Calculus lectures from a professor at MIT in my house or on a walk. What a wonderful time to learn. This program at MIT is truly exceptional.
Even my teens are watching along and getting exposure. Strang is perfect.
+Casey Ryan Agree, he's amazing, especially for someone like me who knew nothing about Calculus. He coaxes you along, something like teaching an animal to trust.
..Dr Strang is enthralling. I would be obscenely jealous of your having for a professor except for two reasons: He got his doctorate at my alma mater, UCLA, and my calculus teacher at UCLA was Dr Matthew Brodsky, an MIT graduate!
You guys do good work.
I GUESS THE NUMBER OF GREAT MATHEMATICIANS IN THE WORLD SHOULD TAKE A LEAP-STEP BECAUSE OF INCREASED ACCESS AND EXPOSURE TO GREAT 'LEARNING MATERIAL' -->MATHLAND
Dr. Gilbert Strang is na outstanding example of what teaching means. Greetings from Brazil.
This is the reason why MIT is a great school to go to. They teach conceptual understanding and ideas instead of a step by step method to solving an equation. It's annoying that teachers dumb down calculus simply as a means to prepare for a test or an exam. This is why we're only as strong as our weakest link. Teachers shouldn't be judged by their flunk rates. Those who want to succeed, will.
..very nice thoughts.
no -
I totally agree with you
that’s right
You said it so true. Every high school teachers including the mentors lower the level of calculus to " Calculus for dummy"
"Letters are not what Calculus is about. It's ideas." - Gilbert Strang
Does he have a Ph.D? Would that make him Doctor Strang?
@@VndNvwYvvSvv he does from UCLA
We're such a lucky generation, i'd think of only 20 years back how it would be hard to reach such understanding.
Big thanks for Prof. Strang for how unique way for teaching the meaning and not the steps !!!!!!!!!
And For MIT open courseWare: you are making the world better :)
I took these courses back in 1987. Love going back (2022) and Prof. Strang is great.
Everything makes Sense. Literally Goosebumps moment. Thanks a ton. Free education empowers you exceedingly. Thanks to MIT and the sponsor. You have impacted many lives, I believe.
I remember this stuff at high school but was completely boring then. I love it now. Feels like Im peering through a keyhole at the secrets of the cosmos.
Thank you Professor Strang for this amazing series on Calculus. I'm a high school student and this was extremely helpful. You've made it so much more easier for people all over the world to gain access to invaluable knowledge through your lectures and God bless you for this!
Your students are lucky that they can become MIT-minded from a young age.
I wish I had come across this series of lectures when (or prior to) starting my calculus one course (I'm almost 31 and only beginning school now, after dropping out [or being kicked out], for all intents and purposes, at age 15)... I was able to understand the "big ideas", so to speak, of what I learned, but they really only clicked after the course ended and I had time to step back and actually play with the ideas. The class was so focused on technical details that it was difficult to see the beauty and cleverness (and actual fundamentally understand) of what is going on.
Of course my algebra skills are, and always have been, dusty; albeit I've been able to ace the GED and placement tests, it was always due more to memorization and brute force than intuitive understanding. These are the same problems I encountered growing up in school; there was rarely a teacher that knew how, or cared to, teach things in a way that would enable you to appreciate what you were actually doing. Not only is this why people tend to be uninterested in math (and technical things) but it is why the teachers and students are ineffective.
Our education system needs some serious re-evaluation.
Thanks for these lectures Professor Strang.
Excellent refresher lecture after many years. Plus, I was excited to learn that the "d" in dy/dx stands for "darn" .
so precise! cutting through whole chapters in just 30 minutes. wow.
Thank you Dr.Gilbert and to the MIT people behind this initiative. This is a perfect example of how much difference an excellent teacher can bring about in the learning process and make seemingly difficult concepts graspable to anyone at all. I have started appreciating calculus so much more.
I'm at the beginning of learning calculus and these videos have been the most helpful thus far! Thank you GS!
With a professor like Mr. Strang, there is no need to ask a bunch of questions in the end. Well explained! …and worth the 30 minutes.
I would have never been math phobic if only I had teachers like Prof.Strang in my school days.
Same.
Does he habe a doctorate? Is he Dr. Strang?
Learned more about calculus in these 30 minutes than in my entire schooling. Dr. Gilbert you are the best. Hats off to you.
This is priceless! Thank you MIT and Professor Strang for making this available to everyone. I took calculus at college but could never really understand the basics in such a clear way. I think the best way for us to return the favor is to share all the things that we know, so people that can´t pay a top-college tuition can access to top quality material.
Not enough time and effort is invested in instilling this “big picture” idea-based understanding. Seems to occur mostly in higher college courses. Great teacher. Wish there were more like him.
Man, if only I looked for MIT open courses before. I would have brushed up on these concepts 5 years ago. Still not late to learn from great professors.
He's so good to listen to. He sounds like a narrator in a documentary. So entertaining!
the best math teacher i ever had
I couldnt believe I was actually enjoying these lectures, and have found myself drawn back into maths "for the fun of it" 10years after leaving college! Thanks dr s. Amazing man.
Just what the doctor ordered. I wanted to delve into my old textbooks, but had lost a lot of the ideas that made sense of them. This was the perfect refresher to get started. Thank you very much!
15 dislikes were by Newton who is jealous of Dr. Strang's awesome ability to teach calculus at MIT!
At first i used to just see x's as x but now i see a whole different meaning to the terms functions, slope etc, thank you professor
Omg, this is the clearest explanation of derivatives ever!! Thank you for the video!
Teachers like this are rare.
the most loaded 6minutes on youtube ever...thank you
Thie professor has a good way of explaning how this works , in the past i studies electronics and learnet this math but never got the feeling that i have after watchting this video , it's very good explained.
So do I, I'm an Electrical Engineer and always is good return to the foundations. Keep in that way!
Thank God I finally got an explanation as to why derivatives work. I missed a day of math for a wrestling tournament and never got it explained to me, and now that year and a half long itch has been starched.
He is amazing. He got his PhD in 1959 and started teaching at MIT before JFK was assassinated and he is still there.
i love how this guy explains the derivative not just tells you how to find it.
Thanks Professor Strang! I was looking at practice BC Calc problems and after watching your video, it demonstrates that Calculus is not just some strange abstract voodoo math with alien derivatives and integrals but just taking algebra to the next level and understandable!
Professor awesome explains what its calculus -- not just solve equations. He explains the reasoning behind the madness. Well done!
This is very helpful for my first year engineering course..
slope and speed are the first prime or the first derivative of a given function. If the car is travelling at y=mx+b, then by applying the power rule of a derivative then it's speed is m. In this discussion, Professor Strang clearly and wonderfully shown to us the concept/idea behind the power rule more than just as nX^n-1. Thank you Professor Gilbert Strang.
thanks to Mr. Strang. Poor people from developing countries now have the chance to have top level education. People like Mr. Strang should be given some kind of noble peace prize not to politicians who pretend to be peaceful but are actually war mongers. God blees Mr Strang wish there were more good people like you.
Greatest Treasures of all times created by MIT and Dr. Strang
I am from a developing country. Since the day I knew the MIT existed I wanted to go there, but I knew It was too difficult. Just 1% in my country make it to go to college. TO GO...and less (much less) than those get a degree. I entered college and was doing great, but after finalizing the secong year I had to quit because I got sick and didnt have enough money. This is like a dream come true in a sense to me. I can attend MIT!!!
perhaps the most interesting video on derivatives on RUclips...:)
Thanks Professor Gilbert Strang :) This videos is really helpful and fun to watch
This guys graphs are perfect.
I love the way this course is presented. I hope I can find more of these videos to cover all of the topics. It is review for me but my first course was not fun to learn.
Thank you so very much Dr Strang! This is really helping me move forward in my college calc prereq! I appreciate the work you put into every video!
It's crazy to think that anyone that understands this lecture has an easy life.
really informational and had a nice experience learning calculus with prof. Gilbert Strang
very informative, thanks
at 3:00 AM in the morning / night .... feeling lucky , this course is an Eye opener .. having my Eureka moments,
Awed by Prof. Gilbert Strang's deep connection with the Mathematics that as if he also re-discovers it every time he lectures ... it is beautiful ....
Thanks for uploading this gold! I'm watching this for my 11th grade exams
Just look at the passion in Prof. Strang’s explanations !! Amazing ...
This is great. You can tell that he his passionate about math, that's one of the most important features about being a teacher. Makes it exciting. =)
His manners are charming and his attempt to make things really clear from the very beginning quite successful. 14:30: the formula of average change is wrong because he writes (Delta x) ^2 over Delta x instead of Delta x^2 over Delta x; he goes further to equate the quotient with Delta x, which is 1 instead of the 3 he had previously computed.
+Navin Sawalani No, sorry, look at the screen. He writes 'average', not 'instantaneous'. Capital delta notation is used for computing the average rate of change. It should be: 'the change in x^2', i.e. 'Delta(x^2)', not '(Delta x)^2', which means 'the square of the change in x'.
***** He is speaking of the average rate of change of the function f(x) = x^2. This is Delta(x^2) / Delta (x). Sorry if I can't understand you. But (Delta x) ^2 / Delta x is just Delta x, of course, and it is simply the change in x, not a rate of change..Thanks, anyway.
Recommend watching at 1.5X speed if you are following along well. It helps save time while getting the full information. Feel free to rewind or pause if you need a minute to process something.
sir you are truly amazing :) my teachers have neglected the understanding of mathematics but it all makes sense now. because of you now i actually understand :)
@18:12-18:16, "This is all algebra now. Calculus is going to come in a moment, but not yet'
The professor carrying the audience into thrilling scene!
Wow, wonderful cognition shift!
I have a question.
So, we have the function y = x²
The slope of this function when x = 1 is 2 (because the derivative is y = 2x).
And the slope when x = 3 is 6?
(We simlly insert value of x in our derivative function?)
Thanks for your wonderful knowledge prof Strang!
Thank you so much Dr. Strang! I love your teaching style and methods... and I appreciate all the hard work of your videos... It has helped me review my calculus skills for Econometrics and Econ Mathematics this semester in grad school. I wish that I could have had you as my original calculus professor! :D You are awesome! :D
Excellent, thankyou.
It handy to know what other parts of calculus one should know. I'm not familiar with the subject.
Thanks Professor Strang! been a very valuable knowledge of calculus for this high school student.
He reminds me of my old physics teacher whom (I have no idea if I just used whom correctly hah) I had in, oh well, 7th grade or so, and he was the one introducing us to atoms and molecules and all that stuff. Everyone thought he was boring and dull, but I think he was a nice guy - just like this guy (: Respect for that old man. And thanks for a great lesson! I've always dreamt of how it was to be at MIT or Harvard or Oxford or anything like that!
After watching this video for 30 seconds, I understand more than what my teachers ever made me understand.
I'm now actually quite angry at how bad teachers I have had. My suspicion is that they did not really understand it, an yet tried to learn others. Not the best idea.
Big thanks for these videos:)
These are nice lectures. It's funny for me to hear a professor begin his lecture by saying "OK, hi" - I am from Europe, where this is not usual.
You have a vastly superior culture, this school is one of America's best and only a few very smart people go there, and have to pay 100,000$ a year to be there!
This is another solid lecture on the way calculus should be taught in beginning.
this is great.. i don't know what to say he has a priceless mind
Excellent sir, Thanks for the help. Concept cleared, Hope in the future I get a teacher just like you.
I`ll call it the beauty of making sence from conceptual ideas .
Thanks so much. This is of such a great help!
“I’m not Rembrandt.”
On the contrary, you are the Rembrandt of linear algebra.
thank you Mr.Strang thank you very much the best video on RUclips :)
I don't want to do my philosophy paper so bad that I'm here studying Calculus haha
Don't go near a bookcase.
Beautiful lecture
This is excellent!
'Calculus is not about letters...it's ideas.' More teachers need to be told this.
function graph slope at different points first increases and then decreaces at peak point and
function derivative give cosin x function whose graph show increase and decreasce in the value of slope of sin function on graph
Nice work professor.
I like that ! Thank you for uploading. Love you.
This is the best mathetics class I ever had! Thank you professor!
Just great explanation
Thank you very much. I was curious what Calculus was about and this lectures really helps. Greetings from Sweden.
Gracias profesor por su enseñanza y gracias a mitopencourseware por su apoyo a la divulgacion del conocimiento para todos los habitantes de nuestro planeta Tierra. El conocimiento de las matematicas nos ayuda a proteger nuestro planeta y a dar bienestar a la gente.
Thanks 👍😊 professor 🙂
thanks for sharing such wonderful knoledge
21:10 I get that 2x + ∆x = 2x if ∆x is very nearly zero. However, how was it possible to get to 2x + ∆x in the first place if ∆x = 0? You'd be dividing by zero, no? I'd be grateful if anybody could explain this.
It is not that Delta x is almost equal to 0 but that we, in computig the derivative of x^2, are interested in the limit of 2x+Delta x when Delta x tends to 0. And this is obviously 2x. Delta x is never 0, it only tends to.
deltaX was never zero but approaching zero So you are not dividing by zero.
2X+ delta X where delta x is so small that it can be excluded.
It's impossible to explain. It's a lie. It's a hack. It's nonsense. You know it's wrong but since our 'teachers' told us we have to religiously follow along.
@@redred4352 No it can't. This is a hack. It's obviously terrible math but we have to victimize ourselves with double think in order to reconcile it.
1. After Find the slope (derivative)
What do you want to achieve
2.Use of slope
It can't be x^2, you are only dealing with one side of the slope, since you are only dealing with one side of the slope it is y=mx+c not y=x^2. x doesn't go on the y-axis. x only goes on the x-axis therefore you can not subtract it believing it is going up the y axis. It should be minus y? How are you evaluating x up the y-axis?
y=f(x) and obviously if x changes a little then y too will change and mathematically we can say y+dy= f(x+dx) which leads to dy= f(x+dx)-y or f(x+dx)-f(x) and soon we can say dy/dx= {f(x+dx)-f(x)}/dx. The only job for the transition for calculus is to apply limits ... and there is the problem.
@TheNoorac e^x is awesome
I enjoyed it (and learned) very much. Tks.
Mr. Strang is a Professor of Mathematics. He has spent a great deal of effort and time working toward a PhD; meaning he's earned the title of, "Dr. Strang". It might seem petty to address him with the proper title, but it's kind of a big deal.
24:40 A small step for man, but a huge leap for Calculus!)
This is helpful, thanks for the upload!!
Its funny how i may be the only business student who has to go through calculus, and not having this in high school just makes it even more harder for me to grasp the basic concepts :(
It depends on the education system.
Sanaa Mohammad ? Depends on that education system? Ok well inside the US, those seeking a bachelors in business admin must take business calculus.
WashingtonMonster86 And in the UK/Australia we don't
Business is all about rates of change (trends) so calculus is essential to have any perspective.
You're not alone...
muy bien saludos me ayudo mucho esta clase profesor saludos.
Great video's! Excellent teachers!
Magician!
,, and A?C power follows the "y=sin x" curve/line.
I like explaining it like this
if f(x) = x^2 then f(10)=100 and f(11)=121 so its up +21
this thing caller a "derivative" lets us estimate the change
d/dx f(x) = 2x which we also write as f'(x)
now f'(x) evaluated at 10 is f'(10) = 20 which is pretty close to 21 (5% err)
it works better with bigger numbers
f(100) = 10000 f(101) = 10201 so its up +201
f'(100) = 200 which is pretty close to 201 (0.5% err)
and it also works better with smaller changes
f(10) = 100 f(10.1)= 102.01 so its up +2.01
f'(10) = 20 so it should go up 20 for each unit of input increase
so 20 * 0.1 = 2 which is pretty close to 2.01
if f(x) = x^3 .......
Thank you thank you thank you so much