@@richardaversa7128 linearization is when you change one or both variables so that the resulting graph is linear, for example a y=1/x graph can be plotted as y vs 1/x instead of y vs x so that it can be analysed without calculus
@@richardaversa7128linear approximation is approximation with tangent line linearization is modifying curved data to make it fit a linear line of best fit
I like these in depth videos, they make you appreciate math more, as apposed to how you learn in high school just rushing through memorizing formulaes and rote learning solutions. Great video!
sorry to be so offtopic but does any of you know a way to log back into an Instagram account..? I was dumb lost my account password. I would love any tips you can offer me!
I finally found out what exactly differential is. I've searched on the internet, read books for a few weeks but I couldn't find a tutorial as simple as yours. I'm gonna pray for you. Thank you so much.
You were correct 100%. (d/dx)() is a function operator that takes a function f as its argument. f has to be a function on x. So (d/dx)(f) is the transformed function. The transformation is defined by the limit of the difference operator, just as you stated. (d/dx)(f) is the same as f'. It's just a different notation. This is ALL that makes the definition of d/dx, nothing else. There is NO multiplication by dx or dy whatsoever because d/dx() is ONE symbol. It's like if a teacher would tell you to divide both sides of the equation sin(2x)=1 by s to get in(2x)=1/s. So, what is done is symbolical manipulations that give you the name of a desired function, e.g. a solution of a differential equation. Hence it's a useful method but the method is formally not mathematical. So, those steps are no more mathematical than, let's say, you make your teacher deliver you a solution of cos(x-sin(×)+sqrt(x))=2 by threatening him to burn his dog. It's a valid and effortless method to get the solution. Once you have it, you can valit it. That threath is a non formally mathematical method just like multiplying by dx. Importantly, we need to consider why the method works. That reason is of course mathematical. In abstract Algebra operations on objects called dx are defined and it is useful. So, there differentials are from a different perspective.
I disagree slightly with the reply above. While (d/dx)(f) is the 'primitive' notion, its existence implies that of the differentials, and the relationship between the two is more than 'symbolical manipulations'. If y = f(x), then the differentials of x and y, 'dx' and 'dy', satisfy the equation dy = dx · f'(x) -- this makes it permissible to swap f'(x) with dy/dx (noting that dx is non-zero). It is customary for dx = Δx. The differentials are then valid objects in their own right, and f being differentiable implies their existence always -- not just 'on the limit'. The important property at the limit of dx → 0 is that Δy and dy coincide; but the value dy/dx can be considered for non-limit values of dx -- this will in general be distinct from Δy/Δx.
Haven't took an intertest in Math ever, even when I was doing this in school. I always came across the Delta symbol in Wiki articles whenever I was looking up information. This defined it quite well.
Thanks. My math teacher just wouldnt tell me what the heck was a dx or dy or d in general (only told me it was differential) This was a good explaining
Thank you sir for posting such great video .I couldn't understand what is the difference between delta and differential.But now iam Clear with that.Such a great explanation ❤
This channel is fantastic, I thought that dx and dy were delta x and delta y when delta x approaches zero. That they really make sense only when they are divided by each other and that we can sometimes use them separately but that was just a math trick. Apparently, dx and dy are not necessarily going to zero, they are just delta x and delta y of the tangent line which is determinate by the derivative. The only thing is that ratio dy/dx has to be equal to the ratio of delta y/delta x in the limit when delta x - >0.
So, to summarize: "Delta" y = dy-h Where h is the difference between two points of a graph/ equation. As h approaches 0, then "deta y" = dy getting + an ever decreasing value [if the limit exists. ]
I am surprised they don't "totally over shoot" like by 10 or more, then reduce to 5, then 2, then 1 to show the actual process of taking a limit. That way you can see it better...
You are out off this world! Amazing understading you have. I love your videos and the way you just explains stuff my teachers never was capable of. Thanks very much.
d(f (x)/dx is a shortway hand of writing delta-y/delta-x when back then they used to find derivatives manually by plugging in delta-x minus h, i recall, they dont have shortcut formula for doing it, now d(f(x)/dy aka dy/dx is now used to implicitly tell that what its doing is approximation
I was wondering if, when deriving equations such as momentum equation in aerodynamics, delta P can also be rewritten as dP since both essentially mean change in pressure?
Hang in there. Most of us did the same. Just keep doing limit problems...at some point, and it's different for everybody, your brain will thoroughly grasp the concept and application.
I understand how you defined dy as the approximate change in y-values of the function, but can you say it is the exact change in y-value for the tangent line at the point dy/dx was calculated on y = root(x)?
The way he defined it, yes. It's exactly like Delta y but for the tangent line function instead of the sqrt() function. In any calculus class you will ever take, no. dx and dy are not variables so we can't plug in numbers for dx and see what we get for dy. We can't even find values for dy and dx since they aren't numbers. They're a notation shortcut for certain equations involving limits.
so Δy/Δx gives the exact slope of a secant line, but only the approximate slope of the tangent line. and dy/dx gives the exact slope of the tangent line, but only the approximate slope of a secant line. maybe I'm wrong but this feels like a succinct way to understand the utilities of Δy and dy and the symmetry between them.
so dy/dx is used if you want to find the straight line right? Like, "if the line doesn't bend because of the √x, where would it be if the starting point is at x=4"
very simple to understand.. thanks dear... but the question i have is.. if taking differentiation of a funtion gives rate of change. and called derivative.. and the reverse is called integration..right?? then it has to be the main function again. why it gives the area under curve??. and in this case the origional function in first place suppose to be the area under curve.
For those not aware, what he described is essentially Linear Approximation, or Linearization
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I'm pretty sure linearization is different
@@rangertato how so?
@@richardaversa7128 linearization is when you change one or both variables so that the resulting graph is linear, for example a y=1/x graph can be plotted as y vs 1/x instead of y vs x so that it can be analysed without calculus
@@richardaversa7128linear approximation is approximation with tangent line
linearization is modifying curved data to make it fit a linear line of best fit
> ∆y is exact change
that would explain why I never have any ∆y when I go to the coffee shop
genius pun right here, give this person a medal
Under rated
???
Give an explanation please
@@solarsystem1958 del y = change
LMAO
I like these in depth videos, they make you appreciate math more, as apposed to how you learn in high school just rushing through memorizing formulaes and rote learning solutions. Great video!
Yay!! I am glad to hear this. Thank you.
Agreed, I hope he does it more and more
I am happy that we have teacher who at least explained this.
sorry to be so offtopic but does any of you know a way to log back into an Instagram account..?
I was dumb lost my account password. I would love any tips you can offer me!
@Ayaan Landyn Instablaster =)
I finally found out what exactly differential is. I've searched on the internet, read books for a few weeks but I couldn't find a tutorial as simple as yours. I'm gonna pray for you. Thank you so much.
and now I finally understand why there's a 'dx' tacked on the end of the dif'd function :D thanks!
got my mind blown recently on that part. why did nobody tell me why it is there before?
@@fruityliciousk2704 Because it is Big american secret!
Holy moly this was so much better than my professors explanation! He literally was trying to explain the concept using marble and bread.
This can be a great introduction into Euler's method as well!
yup!
Interesting, I always understood dy/dx only existed on the limit as Δx approached zero. Anything else was just delta Δy/Δx. ie dy/dx=lim Δx→0 Δy/Δx.
You were correct 100%. (d/dx)() is a function operator that takes a function f as its argument. f has to be a function on x. So (d/dx)(f) is the transformed function. The transformation is defined by the limit of the difference operator, just as you stated. (d/dx)(f) is the same as f'. It's just a different notation.
This is ALL that makes the definition of d/dx, nothing else.
There is NO multiplication by dx or dy whatsoever because d/dx() is ONE symbol. It's like if a teacher would tell you to divide both sides of the equation sin(2x)=1 by s to get in(2x)=1/s.
So, what is done is symbolical manipulations that give you the name of a desired function, e.g. a solution of a differential equation. Hence it's a useful method but the method is formally not mathematical. So, those steps are no more mathematical than, let's say, you make your teacher deliver you a solution of cos(x-sin(×)+sqrt(x))=2 by threatening him to burn his dog. It's a valid and effortless method to get the solution. Once you have it, you can valit it. That threath is a non formally mathematical method just like multiplying by dx.
Importantly, we need to consider why the method works. That reason is of course mathematical. In abstract Algebra operations on objects called dx are defined and it is useful. So, there differentials are from a different perspective.
yes, this is the best way to explain it.
I disagree slightly with the reply above.
While (d/dx)(f) is the 'primitive' notion, its existence implies that of the differentials, and the relationship between the two is more than 'symbolical manipulations'.
If y = f(x), then the differentials of x and y, 'dx' and 'dy', satisfy the equation dy = dx · f'(x) -- this makes it permissible to swap f'(x) with dy/dx (noting that dx is non-zero). It is customary for dx = Δx.
The differentials are then valid objects in their own right, and f being differentiable implies their existence always -- not just 'on the limit'.
The important property at the limit of dx → 0 is that Δy and dy coincide; but the value dy/dx can be considered for non-limit values of dx -- this will in general be distinct from Δy/Δx.
Haven't took an intertest in Math ever, even when I was doing this in school.
I always came across the Delta symbol in Wiki articles whenever I was looking up information. This defined it quite well.
Mate, thank you a lot. I've been reading James Stewart's book for over an hour trying to understand what you've simplified in 10 minutes.
Been reading Thomas Calculus on it & yea same problem.
Thank you so much!
I'm rewatching this video after 6 months. The idea is very clear, and the explanations were understandable. This helps me a lot.
♥
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It was what I needed today.
Impressed with the way you explained such a technical concept with sweet and smiley face
Thanks
Thanks mate by far the easiest explanation vid I have found on UA-cam. You must be a great tutor 👍
I love how you show real uses of theoretical calculus. Liked 😉
I like the graphs you include to assist your instruction and listener understanding.
That cleared out some of my back of the mind doubts
Thank you very much! I am revisiting this topic in Calc 3 and now I get it
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its very useful for me ,ive just confused by the class course ,when i saw this video ,it makes my brain clear again
This makes my concept clear now! Thanks
Yay!!
I’m stuck because I don’t have a calculator with me 😆
I watched your video to learn actually but I suddenly smile when you're looking and smiling at the camera. How cute of you💕
It's amazing your explanation.
Thanks
Thank you for this explanation. It really make me understand better
dy is also a change like ∆y but this change is estimated value. Calculus can pull out very detailed information.
thank you, you make it so easy to understand what exactly does "d"y mean.
Very concise, very understandable. Thanks.
You’re a good teacher. Thanks
Nice content man, it really helped
Thanks. My math teacher just wouldnt tell me what the heck was a dx or dy or d in general (only told me it was differential)
This was a good explaining
Your videos really remind me of just how much I've forgotten. :)
Thank you sir for posting such great video .I couldn't understand what is the difference between delta and differential.But now iam Clear with that.Such a great explanation ❤
Great explanation! Great video.
Bravo!! Crystal clear explanation!!
My boi is slaying the professors with a 10$ mic.
Thank you sir for your clear explanation
Thanks for making the difference clear! :)
thank you very much. now I actually understand what differentiation tells us.
This channel is fantastic, I thought that dx and dy were delta x and delta y when delta x approaches zero. That they really make sense only when they are divided by each other and that we can sometimes use them separately but that was just a math trick. Apparently, dx and dy are not necessarily going to zero, they are just delta x and delta y of the tangent line which is determinate by the derivative. The only thing is that ratio dy/dx has to be equal to the ratio of delta y/delta x in the limit when delta x - >0.
Excellent explanation! Thank you!
U explaination very well u were very cool throughout the video
I really appreciate your hardwork. Thank you.
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐
With the god pen switching technique he also writes so fast that I didn’t see him writing 7:04 “just an approximated”
A man with so much talent !
This is so dope
Loved the explanation, really helped me
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐
This is the best explanation ever! Thank you!
His geometric representation is wrong 😊 go and check mit Herbert gross lecture approximation
Wow, nunca pensé que le entendería a lo que explicaba este man en sus videos, pero me ha servido para la tarea de cálculo xd
Very nice explanation!
Great explanation!
WOW! This is one of the best videos on UA-cam.
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐
Well explained !
Thanks so much for these videos
I can't understand math the way is teach it in school
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Excellent explanations.... 👌👌
Excellent presentation. vow !!
So, to summarize:
"Delta" y = dy-h
Where h is the difference between two points of a graph/ equation.
As h approaches 0, then "deta y" = dy getting + an ever decreasing value [if the limit exists. ]
I am surprised they don't "totally over shoot" like by 10 or more, then reduce to 5, then 2, then 1 to show the actual process of taking a limit. That way you can see it better...
Obrigado pela brilhante explicação.
Can you please share what course are you studying. Your knowledge of calculus is soo coool
You are out off this world! Amazing understading you have. I love your videos and the way you just explains stuff my teachers never was capable of.
Thanks very much.
Trying to learn thank you!!
d(f (x)/dx is a shortway hand of writing delta-y/delta-x when back then they used to find derivatives manually by plugging in delta-x minus h, i recall, they dont have shortcut formula for doing it, now d(f(x)/dy aka dy/dx is now used to implicitly tell that what its doing is approximation
Great video dude!
excellent explanation, excellent
Do one with Sigma and Integral too!!
It's very very clear now. Thank you soooooooo much
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐
I was wondering if, when deriving equations such as momentum equation in aerodynamics, delta P can also be rewritten as dP since both essentially mean change in pressure?
find dy/dx for y^-3/5=sec^-1*sqrtx* 4^lnx / y^2*lnx* tan^-1 *2x i try solving this derivatives .tanks allot
thank you so much, so helpful
😁
Thank You soo much Sir
Thank you. Keep up the good work!
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This is amazing!
finally i've understood the difference betwen derivatives and differential thaaaaaaanks
Can you add 3 or 5 exercises for us to try this and see for ourselves? Thank you.
Thank you sooo much!!!!!
Thanks mate you are amazing
explaining nicely
Thanks a lot sir
thanks, you are my math god
Wow thank you very much!
I dont even have this stuff in school rn, ( going to have it in some weeks) and I already understand smth thank u xd
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐
This video saved my life two times
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐
Thank you Sir....
A student from India...
They skip this in class and say to memorize the formuals...
Im gonna cry right now bc i got a 1.5/10 on my calc test bcz of this thing and you just made my life a lil bit better i cant thank you enough fr
Hang in there. Most of us did the same. Just keep doing limit problems...at some point, and it's different for everybody, your brain will thoroughly grasp the concept and application.
Thank you
can you also compare and contrast with del y?
Thank you.
thank you so much ...
I understand how you defined dy as the approximate change in y-values of the function, but can you say it is the exact change in y-value for the tangent line at the point dy/dx was calculated on y = root(x)?
The way he defined it, yes. It's exactly like Delta y but for the tangent line function instead of the sqrt() function. In any calculus class you will ever take, no. dx and dy are not variables so we can't plug in numbers for dx and see what we get for dy. We can't even find values for dy and dx since they aren't numbers. They're a notation shortcut for certain equations involving limits.
Thanks 🤝
we're now learning integrals, and I have just found out about this today lol
so Δy/Δx gives the exact slope of a secant line, but only the approximate slope of the tangent line. and dy/dx gives the exact slope of the tangent line, but only the approximate slope of a secant line. maybe I'm wrong but this feels like a succinct way to understand the utilities of Δy and dy and the symmetry between them.
Damn. Good thinking
That's a really good way to connect the secant line vs the tangent line.
I want that T-shirt !!!
Wow thank you a lot
: )
This type of videos i want 😀
thank you
so dy/dx is used if you want to find the straight line right? Like, "if the line doesn't bend because of the √x, where would it be if the starting point is at x=4"
THANK YOU
I think it would be better to further include sth in Taylor expansion. For example, the 2nd order derivative and the concept of reminder
Thanks for making my concepts more clear . DrRahul Rohtak
very simple to understand.. thanks dear... but the question i have is.. if taking differentiation of a funtion gives rate of change. and called derivative.. and the reverse is called integration..right?? then it has to be the main function again. why it gives the area under curve??. and in this case the origional function in first place suppose to be the area under curve.
Thank you sm x
This is from 4 years ago.. How did I never know this?!