I've noticed that some people have become confused, complaining that "this isn't differential equations, it's physics." Keep in mind that differential equations were invented to solve physics problems. People also say this is calculus, not differential equations. In reality, calculus is one of the mathematical tools you use in order to solve differential equations. In my video, I purposefully kept the differential equations as simple as possible so as to minimize the use of calculus.
stedwick, your execution of teaching in this short video is excellent, understandable, intelligent, it's perfect and engages me. even the tone of your voice is perfect, very impressive video for dummies like me to understand!
@spacechick88 Variables (axes) can be whatever you want. I felt that "t" for time made perfect sense, and is indeed the usual standard. The y-axis, since it's often drawn vertically, is often used for vertical height. But the bottom line is, you can use whatever letters you want.
While it is commonly the case to use dy and dx for generic cases, it is rather standard for one to use suggestive notation (t for time, d for distance, r for rate and so on) so as to help keep straight what is what while one is working through a problem. As a technical matter though, it is irrelevant what symbols one uses to represent something provided that the symbols are explicitly defined.
This video is so good I didn't notice the Comic Sans until 03:57. Seriously, great video. You cover all of the basics very clearly without any extra or confusing information. Thank you!
This is a great video, thanks. I know this stuff already…but this is such a clear breakdown of everything that it helped reorganize my thoughts. Thank you!!
This is an excellent presentation introducing the reason for the development of differential equations. Just learning how to mechanically work out equations becomes meaningless without the type of background presented here. After looking at the ignorant comments I am left with the impression that the people making them spent too much time playing video games and have lost their ability to actually think. david
I live in the United States, and we use miles per hour, so in order to relate to my students that's what I use. Mathematics is not physics, and as far as this video is concerned, it makes absolutely no difference what the units are, so I choose to use the familiar ones in order to make it easier. Believe me, many students tune out when you start using words like "kilometers" that they have never heard before and will never have to use (as long as they stay in the US).
Sorry for chiming in again, but you may want to specify v(sub i) and then v(sub f) or some relevant syntax; because v-v = 0 (zero). v(sub f) - v (sub i) = (delta) v and divided by the instantaneous time"stamp" differences renders the value of acceleration.
Finnaly I've found someone explaining this using a bit of physics. I'm tired of seeing my school teacher writing "Velocity=Delta X / t" and then when I search about it on the internet, a bunch of derivatives and integrals fly at my face.
@borisjakovljevic , this is kinematics(physics) stuff that I’m learning now. As a 9 year old I have learnt certain topics in algebra/calculus (see my channel page) by using only basic building blocks as integers (+ve & -ve) , fractions, X-table, BEDMAS rule (integers, fractions & decimals). Once I mastered those, any higher level math concept can be learnt & understood using those basic foundations. I’ve just started learning how to solve first order differential equations only at this stage.
Differential equations are based on a mathematical model of CHANGES in our PHYSICAL world. If you don't understand this, differential equation and its symbols will be just ambiguous abstraction that has nothing to do with your universe. This is great explanation if you want to understand it intuitively.
Indeed. It is necessary to say that the values of dx or dt are taken to be infintessimally small, otherwise it isn't instantaneous, it's just Δx and Δt.
Contrary to your disagree as saying this is not differential. It is, it differentiate between to, or it brings one formula as V to give a (acceleration), and the reverse of acceleration to get velocity. The author of the video showing how one formula raises to give the birth of the second, and how you can go back in reverse. This video is a good video that shows the roots or foundation of the idea of differential derived method.
Saying that differential equations are difference equations is a bit of a weird statement to make: students should have a clear understanding between discrete and continuous systems. We use Delta for discrete and d for continuous, so your explanation is a bit strange off the get go.
Excellent! Differential Equations and arriving at solutions or identifying a 3rd variable by identifying 2 known and fixed variables provides a strategy and helpful tactics with regards to critical thinking and applications to Human Resourcing. I should add this video or parts of it's logic to Leadership Continuum training. Thanks!
Not traveling at, accelerating at. It's not a speed, it's an acceleration. Every minute, you are going 14.4 mph faster than you were the minute before.
To be honest, Most high schools after you take Calculus (considering you get up there), you end up taking Statistics. Most "AP" classes only teach up to what in colleges is called "Calc II." Diff Eq is something most people won't see (and need), it is mostly taken by Math, Engineering, Physics, and possibly some Chem majors.
I could see that the constant acceleration is like a pattern, which can be used to know the desired number in any pattern, because patterns are always constant. I just never thought that a difference equation is so general.
I wonder if it might have been better to label the position variable "dy" instead of "dt" as the first derivative is usually written "dy/dx." Also, I believe that he says that position is determined by movement along the x-axis. I was led to believe that the position of an object is indicated via the "y" axis and that the "x" axis is usually reserved to show time. In other words, delta y (the change in position) OVER delta x (the change in time). Someone please correct me if I'm wrong!
@tyson666999 d/dt is Leibniz notation.. I think. I am only learning myself; It is a way of saying "the rate of change of ..something.. with respect to t. dx/dt would be the rate of change of x with respect to t. (d/dx) x^2 = 2x. This means that if you pick a point on x^2 then at that point the rate of change of the function (x^2) would be 2x.
@ManolisPetrakakis I'm amazed by how many people don't understand the difference between math and physics. A differential equation is an "equation" with "differentials" in it, obviously. Physics often USES differential equations, but saying that "that's not math, it's physics" makes no sense at all.
Did nobody else notice that he did the formula completely wrong on the denominator. dt * dt does not equal dt^2. it is (dt)^2. The parenthesis makes all the difference
Good presentation of the fundamental concept of phisics on how to obtain velocity and accelaration, using the position formula. Obviously you needed calculus to diferentiate (derivate), dy/dx or X' x prime. as for other tipe of notation. good presentation and well explained. but calculus is present in the differentiation.
лучше чем меня в институте учили Безклубенко и Балина люди не умеющие учить Thanks mate keep doing in the same way !!! Our teachers at University KNUBiA in Ukraine can not express simply as you can do it !
I think you are mistaken what the author of the video was trying to show. He did go od job in showing differential (difference) of one formula that its result bring up a second formula, and same, you can go back. The two formulas, velocity formula and acceleration formula became differentiated.
It also makes a TON of sense for everybody in the world to speak Esperanto. It's a language designed to make sense, without any ridiculous "exceptions" in the grammar, and think how great it would be if everybody spoke the same language? I could call the entire world stupid for speaking their own, native tongue. But I don't. Of course I believe we should be using standard units, but we don't.
@Zee96969696 Don't you think that "it's not simple enough" and "it doesn't go into enough depth" is kind of an oxymoron? =P You can't have it both ways! I tried to find a happy medium.
Well, actually m/s/s is equal to m/s^2. The way to look at it is (m/s) * (1/s). When you said (m/s)/s, that's actually the same as (m/s) * (1/s). The other with m/s * s is like saying (m/s) * (s/1) = (ms/s) = m. Does this make any sense?
oke, i get that about the students tuning out when they hear kilometers, it just means we in Europe don't tune out that fast. but the time thing, when you design a new system working based in the 10 system i have even more respect for you then i have know.
you can do that to get a simpler value. if you multiply 1/2 by 12/12 which is just 1 you will get 12/24 which equal to 1/2. he is not multiplying by 12 he is multiplying by 12/12 with the up value being poison and the down value being time. and we know that you can multiply any number by 1 as much as you like.
Nice vid! I would suggest, instead of saying "acceleration times time", saying "the product of acceleration and time" for clarity...just a suggestion, awesome anyway. I would also suggest changing your "x" for multiplications to dots, since it's confusing to see it with the "variable x".
I've noticed that some people have become confused, complaining that "this isn't differential equations, it's physics." Keep in mind that differential equations were invented to solve physics problems.
People also say this is calculus, not differential equations. In reality, calculus is one of the mathematical tools you use in order to solve differential equations. In my video, I purposefully kept the differential equations as simple as possible so as to minimize the use of calculus.
This was a great explanation, but it seems to be about differential calculus rather than differential equations.
stedwick, your execution of teaching in this short video is excellent, understandable, intelligent, it's perfect and engages me. even the tone of your voice is perfect, very impressive video for dummies like me to understand!
@spacechick88 Variables (axes) can be whatever you want. I felt that "t" for time made perfect sense, and is indeed the usual standard. The y-axis, since it's often drawn vertically, is often used for vertical height. But the bottom line is, you can use whatever letters you want.
While it is commonly the case to use dy and dx for generic cases, it is rather standard for one to use suggestive notation (t for time, d for distance, r for rate and so on) so as to help keep straight what is what while one is working through a problem. As a technical matter though, it is irrelevant what symbols one uses to represent something provided that the symbols are explicitly defined.
@PauLL95 No, because dt is a single unit, not two separate units. It's like apple x apple = apple^2, not a^2p^2p^2l^2e^2.
That was an introduction to acceleration & velocity, not differential equations! I still have no idea what they are.
you maybe interested in my videos "welearnmath". Watch and subscribe.
i realize Im kinda off topic but does anyone know a good website to watch new tv shows online ?
@Griffin John flixportal :)
@Huxley Mitchell thanks, I signed up and it seems like they got a lot of movies there :D Appreciate it!!
@Griffin John glad I could help :)
05:11
I'd read as: "The change of velocity, over time."
d(dx/dt) / dt
Thank you for the clarity of content!
Thank you Philip this was very well done and easier to understand because of the examples. I wish more people use examples to get the point home
This video is so good I didn't notice the Comic Sans until 03:57.
Seriously, great video. You cover all of the basics very clearly without any extra or confusing information. Thank you!
This is just basic classical physics, not differential equations.
by far this is the best explanation I have seen so far, thank you
This is a good introduction to differential calculus, but not differential equations.
Ohh, uh mean this ia not differential equation....
can please somebody answer me?
At 5:24 we do not need brackets for dt^2? like (dt)^2.
Thank you Mr. Brocoum for the crystal clear explanation. Do you have any such videos on calculus?
i'm so glad people like you upload such useful video like the following on youtube, thank you.
This is a great video, thanks. I know this stuff already…but this is such a clear breakdown of everything that it helped reorganize my thoughts. Thank you!!
This is an excellent presentation introducing the reason for the development of differential equations. Just learning how to mechanically work out equations becomes meaningless without the type of background presented here. After looking at the ignorant comments I am left with the impression that the people making them spent too much time playing video games and have lost their ability to actually think.
david
I live in the United States, and we use miles per hour, so in order to relate to my students that's what I use. Mathematics is not physics, and as far as this video is concerned, it makes absolutely no difference what the units are, so I choose to use the familiar ones in order to make it easier. Believe me, many students tune out when you start using words like "kilometers" that they have never heard before and will never have to use (as long as they stay in the US).
Sorry for chiming in again, but you may want to specify v(sub i) and then v(sub f) or some relevant syntax; because v-v = 0 (zero). v(sub f) - v (sub i) = (delta) v and divided by the instantaneous time"stamp" differences renders the value of acceleration.
Finnaly I've found someone explaining this using a bit of physics. I'm tired of seeing my school teacher writing "Velocity=Delta X / t" and then when I search about it on the internet, a bunch of derivatives and integrals fly at my face.
haha i know that feeling :P :D :(
presentation and teaching was very good. keep moving on and complete my all concepts of differential equations. thanks.
@borisjakovljevic , this is kinematics(physics) stuff that I’m learning now. As a 9 year old I have learnt certain topics in algebra/calculus (see my channel page) by using only basic building blocks as integers (+ve & -ve) , fractions, X-table, BEDMAS rule (integers, fractions & decimals). Once I mastered those, any higher level math concept can be learnt & understood using those basic foundations. I’ve just started learning how to solve first order differential equations only at this stage.
Differential equations are based on a mathematical model of CHANGES in our PHYSICAL world. If you don't understand this, differential equation and its symbols will be just ambiguous abstraction that has nothing to do with your universe. This is great explanation if you want to understand it intuitively.
Indeed. It is necessary to say that the values of dx or dt are taken to be infintessimally small, otherwise it isn't instantaneous, it's just Δx and Δt.
@Stedwick what if it was dt x t? would it be t^2d
In the first step it's very perfect to understand the differential in terms of speed and acceleration.
Contrary to your disagree as saying this is not differential. It is, it differentiate between to, or it brings one formula as V to give a (acceleration), and the reverse of acceleration to get velocity. The author of the video showing how one formula raises to give the birth of the second, and how you can go back in reverse. This video is a good video that shows the roots or foundation of the idea of differential derived method.
Ok, what about the dt^2 - that is dt^2=d.t^2 and not (dt)^2=d^2t^2. So according we should have d^2t^2 in the denominator , right ??
Had the same question
Very well explained about the basics of velocity (dx/dt) and acceleration.
Saying that differential equations are difference equations is a bit of a weird statement to make: students should have a clear understanding between discrete and continuous systems. We use Delta for discrete and d for continuous, so your explanation is a bit strange off the get go.
Excellent! Differential Equations and arriving at solutions or identifying a 3rd variable by identifying 2 known and fixed variables provides a strategy and helpful tactics with regards to critical thinking and applications to Human Resourcing. I should add this video or parts of it's logic to Leadership Continuum training. Thanks!
Not traveling at, accelerating at. It's not a speed, it's an acceleration. Every minute, you are going 14.4 mph faster than you were the minute before.
true, but people write dt^2 and not (dt)^2 out of convenience
This has confused me for 20+ years when I first learned calculus and it took a youtube comment to clarify...SMH
Gravity, is it linear or squared seconds 2, 3 secs respectively. 4:07
9.8+9.8=19.6, 9.8+9.8+9.8=29.4
9.8*2^2=39.2, 9.8*3^2=88.2
To be honest, Most high schools after you take Calculus (considering you get up there), you end up taking Statistics. Most "AP" classes only teach up to what in colleges is called "Calc II."
Diff Eq is something most people won't see (and need), it is mostly taken by Math, Engineering, Physics, and possibly some Chem majors.
I could see that the constant acceleration is like a pattern, which can be used to know the desired number in any pattern, because patterns are always constant. I just never thought that a difference equation is so general.
Nice , more of this kind of topic explanations with practice material from brocoum .
very nice video
I wonder if it might have been better to label the position variable "dy" instead of "dt" as the first derivative is usually written "dy/dx."
Also, I believe that he says that position is determined by movement along the x-axis. I was led to believe that the position of an object is indicated via the "y" axis and that the "x" axis is usually reserved to show time. In other words, delta y (the change in position) OVER delta x (the change in time). Someone please correct me if I'm wrong!
Yes sir I learned from your Vedio which I never get from some others. And what axcetly I looking was. Thanks sir.
@tyson666999 d/dt is Leibniz notation.. I think. I am only learning myself; It is a way of saying "the rate of change of ..something.. with respect to t. dx/dt would be the rate of change of x with respect to t.
(d/dx) x^2 = 2x. This means that if you pick a point on x^2 then at that point the rate of change of the function (x^2) would be 2x.
Hello sir may i know why General Solution(GS) Form is decided?
if roots are same/different of ODE?
Outstanding. Near-perfect elocution is a part of it. Clear graphics another. Breaking it down, then breaking it down further -- all good.
Excellent explanation. I am trying to learn these concepts from the beginning. Very useful video! Thank you!
Thanks I always wondered about differential equations. I am currently in intermediate algebra, i need to take DE eventually for my majors.
@ManolisPetrakakis I'm amazed by how many people don't understand the difference between math and physics. A differential equation is an "equation" with "differentials" in it, obviously. Physics often USES differential equations, but saying that "that's not math, it's physics" makes no sense at all.
Thanks for refreshing my math.Really useful.
how can you know that from 72 up 144 by figuration ? im stock with your graph....help me out ! plz
thx
Sir give me an example of non exact differential equations in which all five rule fail ,five integration factors fail??
I'm sorry? This is not differential equations. You just explained differential calculus, which deals with instantaneous rate of change.
How is dt X dt= dt^2? shouldnt it be d^2t^2
the Leibniz notation (dx/dt) make the derivation easy to understand.. great work thx
o wow so much better than just getting equations and being told when to use them. wish i would have learned this way.
at 03:04 shouldn't it be m/(s*s) and not m/s/s ? since the seconds are multiplied in order to become squared..?
Much better explanation than Indian teachers in 11th standard......
This is great! What program did you use to create the presentation?
Very informative video. Makes Differential Equations seem very easy.
Wonderful explanation!
Did nobody else notice that he did the formula completely wrong on the denominator. dt * dt does not equal dt^2. it is (dt)^2. The parenthesis makes all the difference
thx very much. ..u r someone. ..In fact they need to understand the concept
Good presentation of the fundamental concept of phisics on how to obtain velocity and accelaration, using the position formula. Obviously you needed calculus to diferentiate (derivate), dy/dx or X' x prime. as for other tipe of notation.
good presentation and well explained. but calculus is present in the differentiation.
Sir please tell me which software you used to make this video
Arif khan,
Director, ARIF ACADEMY
INDIA
Thanks for explaination of where the notation of the 2nd derivative comes from. I couldn't find that in my textbook!
Thank you so much. Explanation is very good. I like this video
really good video, explained very well
Thanks Phillip; I'm hopeful that this will help me understand the more abstract and esoteric parts of differential equations - Will
Thanx For uploading this video .. this video seriously helped me alot !
Thank you very much, it's very good explanation for derivative of accelration
Seems application in physics instead of differential equations
Are you suggesting that differential equations are no used in physics? Eish...
@Stedwick Are you an engineer, teacher, or some sort of a scientist?
Why did u multiply it by 12 plz if u can explain ? Thanks. Also why is it an unusual speed ?
this did not help me understand differential equations, it was just a good example of deriving velocity and acceleration from positions
Awesome presentation with clarity
Thanks Much.. I got a very clear idea on Differential equations.. Nice Video.. :)
what is the purpose of d when explaining v over t, does it even need to bee there
лучше чем меня в институте учили Безклубенко и Балина люди не умеющие учить
Thanks mate keep doing in the same way !!!
Our teachers at University KNUBiA in Ukraine can not express simply as you can do it !
Thank you for the video, very helpful in recollecting my memories on this stuff! :D
excellent sir.. explained in a very simple way
I think you are mistaken what the author of the video was trying to show. He did go od job in showing differential (difference) of one formula that its result bring up a second formula, and same, you can go back. The two formulas, velocity formula and acceleration formula became differentiated.
This is just basic kinematics. What does it have to do with differential equations?
WOW!!! excellent brief explanation! Thanks a lot.
It also makes a TON of sense for everybody in the world to speak Esperanto. It's a language designed to make sense, without any ridiculous "exceptions" in the grammar, and think how great it would be if everybody spoke the same language? I could call the entire world stupid for speaking their own, native tongue. But I don't.
Of course I believe we should be using standard units, but we don't.
Thank you sir for your clear explanation 😊
@Zee96969696 Don't you think that "it's not simple enough" and "it doesn't go into enough depth" is kind of an oxymoron? =P You can't have it both ways! I tried to find a happy medium.
i love the way you teach bat with the velocity how did you get 48mph
you maybe interested in my videos "welearnmath". Watch and subscribe.
Well, actually m/s/s is equal to m/s^2. The way to look at it is (m/s) * (1/s). When you said (m/s)/s, that's actually the same as (m/s) * (1/s). The other with m/s * s is like saying (m/s) * (s/1) = (ms/s) = m. Does this make any sense?
excellent video for introduction to differential calculus... nice
Great explanation and more power
@ 05:27 - shouldn't it be dt X t = dt2?
Cause dt X dt = d2t2
This is what I am looking for. The principle/whatz going on behind tedious Calculus calculations. Thankz a lot. ^^
you maybe interested in my videos "welearnmath". Watch and subscribe.
I Really Like The Video Differential Equations Introduction From Your
oke, i get that about the students tuning out when they hear kilometers, it just means we in Europe don't tune out that fast. but the time thing, when you design a new system working based in the 10 system i have even more respect for you then i have know.
oh oh excellent explanation i luved this so helpful thank you
you can do that to get a simpler value. if you multiply 1/2 by 12/12 which is just 1 you will get 12/24 which equal to 1/2. he is not multiplying by 12 he is multiplying by 12/12 with the up value being poison and the down value being time. and we know that you can multiply any number by 1 as much as you like.
I have cleared my problem from this video thanks
excellent explanation about velocity, acceleration and gravity but not differentiation!
Nice vid! I would suggest, instead of saying "acceleration times time", saying "the product of acceleration and time" for clarity...just a suggestion, awesome anyway. I would also suggest changing your "x" for multiplications to dots, since it's confusing to see it with the "variable x".
Man, you are a hero.
great staff right there so helpful like thay
You made it easy brother :) thanks.