Math: Differential Equations Introduction

[@PhilipBrocoum]

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.

[@iAmTheSquidThing]

This was a great explanation, but it seems to be about differential calculus rather than differential equations.

[@RedTriangle53]

This is just basic classical physics, not differential equations.

[@mrrobotica]

This is a good introduction to differential calculus, but not differential equations.

[@hafsaimtiaz5832]

Ohh, uh mean this ia not differential equation....

[@SubaddraSankruti]

Thank you Mr. Brocoum for the crystal clear explanation. Do you have any such videos on calculus?

[@aliquewilliams3080]

I'm sorry? This is not differential equations. You just explained differential calculus, which deals with instantaneous rate of change.

[@engineerSalih]

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.

[@amandadube156]

That was an introduction to acceleration & velocity, not differential equations! I still have no idea what they are.

[@DRCSUDHAGAR]

you maybe interested in my videos "welearnmath". Watch and subscribe.

[@griffinjohn3232]

i realize Im kinda off topic but does anyone know a good website to watch new tv shows online ?

[@huxleymitchell5407]

@Griffin John flixportal :)

[@griffinjohn3232]

@Huxley Mitchell thanks, I signed up and it seems like they got a lot of movies there :D Appreciate it!!

[@huxleymitchell5407]

@Griffin John glad I could help :)

[@glaucomachadocaon5029]

05:11 I'd read as: "The change of velocity, over time." d(dx/dt) / dt Thank you for the clarity of content!

[@kynigh]

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.

[@mukulsharma5738]

haha i know that feeling :P :D :(

[@taurusgemini4792]

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

[@TheLuminousOne]

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!

[@PhilipBrocoum]

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).

[@postholedigger8726]

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

[@PhilipBrocoum]

@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.

[@gerald_the_science_guy]

does this guy even know what differential EQUATIONS are??

[@ammomalik9925]

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.

[@DmitriNesteruk]

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.

[@CocoGras]

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!!

[@elranitya]

Very well explained about the basics of velocity (dx/dt) and acceleration.

[@Biswadeepable]

Much better explanation than Indian teachers in 11th standard......

[@sahibgasimov4907]

In the first step it's very perfect to understand the differential in terms of speed and acceleration.

[@bstrain08]

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!

[@PhilipBrocoum]

@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.

[@integralmath]

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.

[@Avionics1958]

by far this is the best explanation I have seen so far, thank you

[@MaV3RiKx]

o wow so much better than just getting equations and being told when to use them. wish i would have learned this way.

[@davidkrowa4153]

this did not help me understand differential equations, it was just a good example of deriving velocity and acceleration from positions

[@LOTIL62]

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.

[@warronfrench8163]

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.

[@longdragon3]

i'm so glad people like you upload such useful video like the following on youtube, thank you.

[@enthusiastmathkid]

@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.

[@ottosparky]

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.

[@vikiboyable]

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 !

[@nidurnevets]

Excellent explanation. I am trying to learn these concepts from the beginning. Very useful video! Thank you!

[@theclint88]

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.

[@amannvig]

Nice , more of this kind of topic explanations with practice material from brocoum . very nice video

[@hsiehkanusea]

Outstanding. Near-perfect elocution is a part of it. Clear graphics another. Breaking it down, then breaking it down further -- all good.

[@johndoe917]

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.

[@trommelbiel]

Thanks for refreshing my math.Really useful.

[@samirnaikwadi3761]

presentation and teaching was very good. keep moving on and complete my all concepts of differential equations. thanks.

[@TheEleventhIndian]

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!

[@jameserayburn]

Wonderful explanation!

[@Mathbihi]

the Leibniz notation (dx/dt) make the derivation easy to understand.. great work thx

[@spacechick88]

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!

[@ammomalik9925]

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.

[@PhilipBrocoum]

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.

[@baderalharbi2624]

thx very much. ..u r someone. ..In fact they need to understand the concept

[@shrinathm.g.8183]

Awesome presentation with clarity

[@GkNs05]

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.

[@charan305945]

excellent sir.. explained in a very simple way

[@paesanng]

This looks like maths for the masses.

[@mhj.xd7]

excellent video for introduction to differential calculus... nice

[@venkatmanikyala4810]

Thank you so much. Explanation is very good. I like this video

[@PhilipBrocoum]

@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.

[@loveislam9174]

I have cleared my problem from this video thanks

[@shohelbd8931]

Yes sir I learned from your Vedio which I never get from some others. And what axcetly I looking was. Thanks sir.

[@M07RealKing]

Man, you are a hero.

[@atomgonuclear]

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

[@LuisMunozCompScience]

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.

[@jasoncater5737]

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".

[@chestypants78]

Great video, very clear. Except, for the 'end v = 144' part. You just skipped past it. Would I be right in saying that x.t.v= 12x10x1.2= 144?

[@PhilipBrocoum]

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.

[@warronfrench8163]

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.

[@tumbashdewan9409]

excellent explanation about velocity, acceleration and gravity but not differentiation!

[@knuid]

Thanks for explaination of where the notation of the 2nd derivative comes from. I couldn't find that in my textbook!

[@asmcriminaL]

Thanks I always wondered about differential equations. I am currently in intermediate algebra, i need to take DE eventually for my majors.

[@William_sJazzLoft]

Thanks Phillip; I'm hopeful that this will help me understand the more abstract and esoteric parts of differential equations - Will

[@sdsuengr24]

This is great! What program did you use to create the presentation?

[@matey114477]

It has nothing to do with differential equations.. very bad

[@F1ST2BULLET]

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.

[@adam3141]

@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.

[@Smeak686]

Very informative video. Makes Differential Equations seem very easy.

[@Erock691]

Thank you for the video, very helpful in recollecting my memories on this stuff! :D

[@balajiprasannamy4995]

Thanks Much.. I got a very clear idea on Differential equations.. Nice Video.. :)

[@13queencoffee72]

This is what I am looking for. The principle/whatz going on behind tedious Calculus calculations. Thankz a lot. ^^

[@DRCSUDHAGAR]

you maybe interested in my videos "welearnmath". Watch and subscribe.

[@jbong9421]

Great explanation and more power

[@hannahnelsonjasper6022]

Thank you sir for your clear explanation 😊

[@FakeAssHandsomeMcGee_]

dy/dx = "lim delta y/delta x". delta x->0 I think that it is just rewritten so that it won't include the limit and stuff sort of like the definite integral and the Riemann Sums. That s the way that it is written in the textbooks and everywhere else I go leads me to the same definition. I hope I am helpful if not, I am really sorry. I had the same problem with delta y/ delta x and dy/dx before.

[@robertfaney4148]

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 ??

[@booJay]

Had the same question

[@shrinathm.g.8183]

Nice one. Topic of video to be named appropriately

[@joes5591]

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

[@ahmadalwazzan384]

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.

[@imegatrone]

I Really Like The Video Differential Equations Introduction From Your

[@saadfarhanali4989]

Thank you very much, it's very good explanation for derivative of accelration

[@jonathanmutema323]

great staff right there so helpful like thay

[@Arycke]

I like the rate of change of acceleration because it is jerk, the third derivative of the position function x :)

[@abrasivepaste]

I think im goning to show this to my math teacher. he'd love it. as do I.

[@Prinoto]

Oh and yes, that made sense. It was pretty much what I was thinking hence why I said; Either it's (m/s)/s or m/s*s

[@SumantKumar-qt1gi]

thanks sir I have cleared my problem from this video

[@physicskid1]

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?

[@eightfivezerobraxton5509]

really good video, explained very well

[@inspiration7]

Seems application in physics instead of differential equations

[@mrjnutube]

Are you suggesting that differential equations are no used in physics? Eish...

[@paulhetherington3854]

Signa df(xt) -- cell num = formula. No division - calculus rule. Grids - are fixed - in VARs dx.

[@starponys0740]

I believe this video and mine ("Calculus for 6th Graders") greatly complement each other.

[@qzorn4440]

I was passing a car on ice at a (dx/dt) that made my calculations incorrect. Nice Lec.

[@PhilipBrocoum]

@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.

[@darkspace08]

WOW!!! excellent brief explanation! Thanks a lot.

[@rajandaniel24]

You made it easy brother :) thanks.

[@mukulsharma5738]

Thanx For uploading this video .. this video seriously helped me alot !

[@almog788]

This is just basic kinematics. What does it have to do with differential equations?