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.
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.
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!
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).
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.
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
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.
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.
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.
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!
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
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 !
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.
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 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!!
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.
@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.
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!
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 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.
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!
The label for this video is not accurate. An accurate label would be: Introduction of Differential equations for the lay person. Mr. Brocoum makes this clear at the beginning of the video, by stating that the view does not need to know any Calculus to follow along. Listening to the lecture the listener will find a clear and concise explanation on the concept of initial and terminal positions with respect to time. This is an excellent explanation of what calculus, specifically differential equations have for practical application in the real world for a lay person who hears the words: Differential equations. Good explanation and clear presentation. Need to re- label the video. Thank you.
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.
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.
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.
@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.
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.
Around t=1m8s you said multiplying by 12 gives 48mph; you should have stated a factor of 12 over 12. Simply multiplying by 12 renders a value of 48mi/5 minutes. We are talking about details and it is our jobs as engineers and scientists to solve problems and provide the detailed solutions to them.
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.
Matej Velko yes it does. Mechanics is the easiest way to explain differential equations as it takes away the abstraction of graph based methods and applies it to real world scenarios that beginners can use.
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.
@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.
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?
@Stedwick I would have to disagree with your statement about it being an oxymoron. The more in depth you go in maths, the easier it gets. When the' why?' is explained, maths becomes so much easier. It is easier to understand how and why something works rather than to trying to memorize formulas and trying to memorize ways of solving a problem. Because there are thousands of different types of problems, it is important to understand what is going on.
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.
This is just basic classical physics, not differential equations.
Thank you Mr. Brocoum for the crystal clear explanation. Do you have any such videos on calculus?
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.
@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.
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!
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).
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 :)
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.
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
05:11
I'd read as: "The change of velocity, over time."
d(dx/dt) / dt
Thank you for the clarity of content!
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
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.
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.
Much better explanation than Indian teachers in 11th standard......
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.
i'm so glad people like you upload such useful video like the following on youtube, thank you.
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!
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
by far this is the best explanation I have seen so far, thank you
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 !
Very well explained about the basics of velocity (dx/dt) and acceleration.
I'm sorry? This is not differential equations. You just explained differential calculus, which deals with instantaneous rate of change.
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.
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 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!!
Outstanding. Near-perfect elocution is a part of it. Clear graphics another. Breaking it down, then breaking it down further -- all good.
In the first step it's very perfect to understand the differential in terms of speed and acceleration.
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
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.
@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.
this did not help me understand differential equations, it was just a good example of deriving velocity and acceleration from positions
Thanks for refreshing my math.Really useful.
Excellent explanation. I am trying to learn these concepts from the beginning. Very useful video! Thank you!
Yes sir I learned from your Vedio which I never get from some others. And what axcetly I looking was. Thanks sir.
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!
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
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".
This is great! What program did you use to create the presentation?
o wow so much better than just getting equations and being told when to use them. wish i would have learned this way.
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.
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!
The label for this video is not accurate. An accurate label would be: Introduction of Differential equations for the lay person. Mr. Brocoum makes this clear at the beginning of the video, by stating that the view does not need to know any Calculus to follow along. Listening to the lecture the listener will find a clear and concise explanation on the concept of initial and terminal positions with respect to time. This is an excellent explanation of what calculus, specifically differential equations have for practical application in the real world for a lay person who hears the words: Differential equations. Good explanation and clear presentation. Need to re- label the video. Thank you.
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.
Nice , more of this kind of topic explanations with practice material from brocoum .
very nice video
really good video, explained very well
This looks like maths for the masses.
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.
Thank you so much. Explanation is very good. I like this video
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.
Very informative video. Makes Differential Equations seem very easy.
Awesome presentation with clarity
the Leibniz notation (dx/dt) make the derivation easy to understand.. great work thx
thx very much. ..u r someone. ..In fact they need to understand the concept
@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.
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.
Wonderful explanation!
Around t=1m8s you said multiplying by 12 gives 48mph; you should have stated a factor of 12 over 12. Simply multiplying by 12 renders a value of 48mi/5 minutes. We are talking about details and it is our jobs as engineers and scientists to solve problems and provide the detailed solutions to them.
Man, you are a hero.
Thanks I always wondered about differential equations. I am currently in intermediate algebra, i need to take DE eventually for my majors.
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.
excellent sir.. explained in a very simple way
Thanks Phillip; I'm hopeful that this will help me understand the more abstract and esoteric parts of differential equations - Will
@Stedwick Are you an engineer, teacher, or some sort of a scientist?
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
Thank you very much, it's very good explanation for derivative of accelration
Sir please tell me which software you used to make this video
Arif khan,
Director, ARIF ACADEMY
INDIA
Sir give me an example of non exact differential equations in which all five rule fail ,five integration factors fail??
Hello sir may i know why General Solution(GS) Form is decided?
if roots are same/different of ODE?
excellent video for introduction to differential calculus... nice
I Really Like The Video Differential Equations Introduction From Your
excellent explanation about velocity, acceleration and gravity but not differentiation!
does this guy even know what differential EQUATIONS are??
Thanx For uploading this video .. this video seriously helped me alot !
I have cleared my problem from this video thanks
It has nothing to do with differential equations.. very bad
Matej Velko yes it does. Mechanics is the easiest way to explain differential equations as it takes away the abstraction of graph based methods and applies it to real world scenarios that beginners can use.
Why did u multiply it by 12 plz if u can explain ? Thanks. Also why is it an unusual speed ?
Great explanation and more power
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.
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.
How is dt X dt= dt^2? shouldnt it be d^2t^2
I think im goning to show this to my math teacher. he'd love it. as do I.
Thanks for explaination of where the notation of the 2nd derivative comes from. I couldn't find that in my textbook!
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.
Sir I am Javaid Qureshi from Lahore Pakistan, I want to learn differential equation & integration,
How I learn now at the age of 52 years.
@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.
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?
I was passing a car on ice at a (dx/dt) that made my calculations incorrect. Nice Lec.
I believe this video and mine ("Calculus for 6th Graders") greatly complement each other.
Oh thank you so much! You are so much better them my teacher!!!
Thank you sir for your clear explanation 😊
Signa df(xt) -- cell num = formula. No division - calculus rule.
Grids - are fixed - in VARs dx.
Nice one. Topic of video to be named appropriately
Thanks Much.. I got a very clear idea on Differential equations.. Nice Video.. :)
@Stedwick I would have to disagree with your statement about it being an oxymoron. The more in depth you go in maths, the easier it gets. When the' why?' is explained, maths becomes so much easier. It is easier to understand how and why something works rather than to trying to memorize formulas and trying to memorize ways of solving a problem. Because there are thousands of different types of problems, it is important to understand what is going on.
oh oh excellent explanation i luved this so helpful thank you
Thank you for the video, very helpful in recollecting my memories on this stuff! :D