This is why you're learning differential equations
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- Опубліковано 12 тра 2024
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When I teach about differential equations, I'll make sure to do a similar introduction, it's really brilliant
Speaking of brilliant, this comment is sponsored by...
In my opinion there are way easier and more general examples to use, for learning about differential equations. 3blue1brown has done a great job in that regard. I very much prefer the classic pendulum and heat-transfer as starting points. Just not the chase curve. But this might be just my personal preference.
Why use "d" why not use the delta symbol?
Delta is for partial derivatives
@@gsjxbxbxhdhs5352 Nord vpn
them: do you even lift bro?
me: yes. barbells, with no mass.
Lel
@FullTimeSlacker lololo
It's impossible, technically.
@@chandrakumar2940 r/whoosh
It is not considered in the equation because the mass of the barbells ain't changing. So for the sake of simplicity in an already complex equation for the general masses, they've been left out.
When I learned physics at University one of the most satisfying experiences was getting to grips with calculus enough to use it to derive equations as it allowed me to wield mathematics to describe the world, which felt awesome.
Dont click his link,its most likely scam
@@nq5044 most likely, they’ve placed this exact comment in other comments in this channel
Lies again? Dear RJ
The reason I like math now. Back in high school they made it too grindy for me, but now I'm loving it as the grind pays off little by little.
I feel like Goku sometimes
And God said let there be dx
Me wanting to be an engineer: Haha, I'm in danger
Just keep practicing your math. Calculus may be challenging but it is really useful.
@@wyattb3138 I know, but my braincells are in danger fellow engineer
Spectrum Night, apart from doing all the math, engineering really depends on your creativity and being able to think of unique solutions to problems. After all, engineering is just problem solving.
Trust me.iam engginer .wtf just happen here
Laughed, well this shit it's hard and endless, don't know how to interiorize it
"Let's assume there's no wind"
When have I seen this line before..
Oh yeah!!!
"Neglect friction"
"Air resistance can be ignored"
"Gravity free space"
"Energy loss is negligible"
"Disregarding relativistic effects"
"Ignoring quantum effect of electrons"
" sin(θ)=tan(θ)= θ "
Sounds familiar, huhhhh
@@anujbangad3973 Aaahh, the noturious sin(x) = x. Just go ahead and put a 3 for pi and e while you're at it
@@simonhallin8909 Don't forget to assume the cow is spherical!
@@simonhallin8909 pi square is g
@@tarunbalchandbhaimulchanda6929 of course! But i prefer using e^2 instead
I asked my Math teacher the same question when he was teaching DE. And the whole class laughed at me. Thanks for the video.
Obviously while you were studying the text they were catching up on the latest season of Numb3rs. Study smarter, not harder! :D
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.wsep
Bcoz u were studying for knowledge and they were studying to pass an exam
Fools
I'm 1 year late but this happened in my class yesterday, everyone laughed not at the student but with him because it sounded like they were funnily teasing the professor.
One of the best videos ive seen, it gave me some sort pf motivation to finally pay attention in math class since my teacher never explains why we are learning what we are learning
a) cuz you will do more complex maths later and you will needs this building block
b) cuz it's on the test next month
These are the only reasons ever given to me.
Truly, school math is only interesting to autists.
for real, mine just tells us one method of solving it, doesn’t tell us how it works, and calls it good 😮
I doubt even the teacher fully understood why he was teaching what he was.
Differential Equations are definitely a household name in the applications of maths. They are really fun when you know how to utilize all of their techniques. Awesome work!
omg yes! Diff EQ should be taught way earlier so students of math can see how all the "useless shit" they learn comes to life!
Just a question, i'm currently in 11th grade and I want to ask is there literally any application of those trigonometry identities that you had to memorize in high school? Cuz I have probably memorized 40 of them and it's driving me crazy!
@@livethefuture2492 I believe that Trigonometric Identities are absolutely critical for things such as buildings and architecture, trying to find the lengths and angles of certain objects, as well as finding the existence of 0, 1, or even 2 possible triangles. It's also very useful in Engineering, understanding the use of currents.
@@CBielski87 I think Differential Equations are something that someone really wants to do in order to really do it. They absolutely have their purposes, but it's something that you need to understand years of calculus and advanced math to really understand.
@@livethefuture2492 Trigonometry is fundamental in any engineering or scientific field. You have to memorize the basic identities and equations, because you'll use them a lot and frequently so you can't demonstrate them anytime, BUT you have also to understand their meaning.
Good to know Zach :D
I thought you liked integration more :D
Hey papa!
@Flammable Maths , 57 is the goodest prime number :)
Numerically, you never derive, you integrate.
I'm not sure what the narrator is trying to say at 6:00, but that's not a differential equation in the usual sense at all, but actually a *differential inequality* ... it is generally true for any two vectors that 𝐀⁄|𝐀| · 𝐁⁄|𝐁| = 1 ⇔ 𝐀·𝐁 > 0 . So, all the problem stated at 6:00 is actually saying is that (𝐦 - 𝐜)·d𝐜⁄dt > 0; i.e. 𝐦·d𝐜⁄dt > 𝐜·d𝐜⁄dt. If the additional assumption |𝐜|² = 1 is being made, then since 𝐜·d𝐜⁄dt = d/dt (|𝐜|²/2) = 0, then the inequality reduces to 𝐦·d𝐜⁄dt > 0. *Any* unit vector 𝐜(t) function of time (i.e. |𝐜(t)|² = 1) for which 𝐦(t)·𝐜'(t) > 0 is a solution to the problem.
When I studied aeronautical engineering at university I was amazed when I discovered that DE are the key to model many physical problems no matter if it is structural mechanics, thermodynamics, aerodynamics or electrical engineering.
In which semester are you?
I am learning differential to slap my brother perfectly at the moment when he would be running to tell my mom that I failed in math.
lmao
Same bro, but instead of brother, cousin.
@@sheepeeeyming8698 Your cosine?
@@Takin2000 so funny😂
@@Takin2000 bruh
Had a similar chain problem on a physics exam. Still haven't recovered mentally/emotionally.
oh god i'm afraid of AP Physics a little now, at least toward the end of the year. I really only know the most basic information about movement and forces. I'm doing calc at the same time, so I don't even know that math. Hoping the class doesn't kick my ass too hard lmao
Edit: It did, it did kick my ass
@mozart mechanics
Diondre Dunigan you are fine, AP Physics 1 or 2 does not use Calculus, So you won’t see any differential equation problems. AP Physics C does use calculus however so if your taking AP physics C, but I doubt you would see difficult differential equations there. The math in AP physics 1 or 2, is not intensive at all so I wouldn’t worry!
@@biplovebaral8755 Thank you so much! I am taking AP Physics C, but it really all depends on what my school's curriculum is like in terms of physics. I passed my precalc class this year with an A, but my Trig class... You wouldn't think Trig/Algebra two quizzes could be so difficult, but my teacher made them so. But thanks for letting me know!
They give us this question in med school exam in India
"Differential equations are cool"
~Big Bang
"Yeah really cool"
~Big Freeze
Big bang, come on
"nothing was ever anywhere, makes sense right? like I said it didn't happen" - bill wurtz
The big bang is a hoax dont be decieved.
@@davidedmundtochi5228 I bet your one of those religious people right?
You know, I really enjoyed calculus last year and understood many of the real life applications, but I never knew about the pursuit curve thing before. Mathematics is just something else man.
What's going on my Liege
Ikr math is so cool it feels like I'm a seer discovering the mysteries of the universe
Me: Why are we learning this?
Teacher: So, that's how you're going to solve it when it appears in examination
Me: 🙃
The way school teaches maths is clever
They have selected the most possibly inefficient way after not teaching at all
🤣🤣🤣🤣exactly
@@maxwellsequation4887 Best comment.
Thank you for saying this.
Me watching this, avoiding actually learning the differential equations.
I've got an exam in differential equations in 3 days and your comment felt so close to my heart this moment haha
@@wojtekkowalski7403 😫😫😫😫😪😪😪
Today i got exam on differential equation, grade 12.
It's kinda easy to solve them but my school didn't teach any application of this. The problems are too long it's exhausting
google is tracking you
@@mosaicbrokenhearts2886 This is pretty much reason why it sucked in highschool. We were not having any context. They just said: "'Solve this"
Now when I'm studying engineering, we have context but its so damn hard because I did not learn it in high school.
gravity rounded to 10
* Laughs in physics *
Straight up paused the video at that moment and went straight to comments. As an engineer, this hurts my body and soul.
@@seriyooow310 same
@@seriyooow310 Wait don't engineers approximate e as 2 and π as 3, and g as π²?
g=9,81 m/s period
Me acting as if I understood anything he just said: 🤓🤓
I love how intuitive he is with explaining it, it's easier to understand why it's important and gives it meaning.. something few ppl do but it seperates the good from not so good at explaining things
People who like math: wow this is interesting
Me, who barely passed calc 2 and linear Algebra: *screeching noises*
I wanted to be an engineer. I can't number. So I went to biology lol
@Bernd DasBrot like hell it's not
Me who didnt memorize the multiplication tables because yes and then didn't know how to do division:
*Intensive sweating*
C's get degrees
Lol I baaaarely passed calc 1 and failed linear algebra
4:10 There's this famous example of a pursuit curve.
The French wanted to make an anti ship missile.
So they built a missile, slapped on a sensor, and then programmed the missile to always fly towards the target.
In the first test, they launched against a *small* "drone" target.
As the distance approached 0, the tightness of the turn required to remain on target approaches infinity.
So it missed.
It now locked on to a stationary buoy.
But the buoy was WAY too *small* for the missile to hit, so it missed.
Finally, it locked on to a *large* civilian cargo ship, which was minding its own business.
The testers panic, because that ship is in range, it's so large they think the missile WILL hit, and they didn't bother to install a remote termination system.
The missile again lowers its altitude to the sea skimming attack pattern.
It makes the last course adjustments...
...and misses.
Finally it runs out of fuel and crashes into a busy shipping lane.
When Sweden's FOA (defence research institution) learnt of this, they fed the missile's guidance algorithm into their brand new (for that time) supercomputer, and the output predicted the exact flight pattern of that French missile.
That was when the French leant about "CBDR-pursuit" (Constant Bearing Decreasing Range) and "PIP-guidance" (Predicted Impact Point).
Holy shit. That is crazy!
@@manikanta2000 doesn't take that long tbh
@@manikanta2000 i know i know
yay weapons of war
@@manikanta2000
It had a buildup, climax, cliffhanger, resolution and lessons learned in like a 60 second read. Worth.
Knowing why I will be taking Diff Eq. this coming semester is half the battle. Everything you covered was very interesting to me and now I'm looking forward to taking the class and expanding my knowledge. Thanks for the informative video!
I wish i had this UA-cam when i went to school.
People like you make the most valuable part of it, amazing.
Thank you!
DEs was always one of my favorite courses
It started out looking good for me but I quickly spiraled down. Have never recovered since then.
Wondering video illustrating not simply the awesome power of calculus, but the concept as well. The conceptual thinking here is key as this is how we begin to develop models for analysis!
wow i am feeling great to have found about a channel dedicated to application rather than only to theorem which we can easily find in textbook. KEEP IT UP!!!
I feel like if I knew the application of differential equations, I would have enjoyed that course much more. This video makes me want to revisit those concepts. Thanks.
You just didn’t have the drive
It's no different than other math logic. Y=X+1 for example is a very basic expression. You can instantly explain it since it's so simple. But if you change it so Y=1+dx/dt, then we have a Y which is going to be different in the same system for every sample we take of x in the timeline (see how sneaky it is?). We simply take the two dimensional space and move it across the timeline in order to get a function in time. This is literally all there is to it, but written down in a single line for convenience. You don't want to write a hundred lines for a hundred samples of X now do you... Newton probably got pissed by this exact thing. I'm no Newton and the idea of such a tedium pisses me off.
Great video, I took differential equations as an undergrad pre-requisite to mechanical engineering at UT. We called it 'difficult equations', but made sense when I later got into applications (i.e. state space model diff. eqs.).
Im in my last Calculus 3 class taking Diff Equations next semester and this looks pretty interesting, I can't wait! Thank you for the vid Zach!
well....how'd it go...?
@@jasonfarrell00 I'm in the same boat but I just passed Calc 3 and my Diff Eq starts in 4 weeks
@@MaximusLX best of luck to ya! i was outta school for a few years then came back and went right into diff eq lol it was rough. but coming right out of calc 3 should put you in a great spot to do well 👍
Bruh im doing both in same semester hahaha
Out of all my math classes. Diff EQ is my favourite. It was fun figuring things out and having it all come together
@Zach Star Thank you for presenting these awesome real-world applications of differential equations! It really helps to understand how to apply the mathematics that we learn or are going to learn. Please keep the educational and informative videos coming. I really appreciate what you are doing.
- This was way over my head but I enjoyed how you presented it. The equation for constant change in mass as the shuttle rises instead of Newtons really struck me to how complicated a launch is. 🤔 👍
Thanks for making me dread this next semester a little bit less haha. Love you’re comedy videos but I think I love the teaching ones even more!
Zach, Just brilliant. I am always curious about the implications of the math I am learning. Thanks a lot
Just like how grass is always greener on the other side, everybody likes to say that their education systems are bad etc. But I'm so glad that our state school syllabus (Indian) had a chapter in 12th Maths called "Application of derivatives" and it taught us practical applications of differential equations. It had problems very similar to those shown in the video. Motion of a rocket with time varying mass, filling up of conical containers with time varying radius, maximizing volume of solids for given surface areas, etc. And I must say, that is what really made me fall in love with differential equations. I just laugh at people who say "When am I ever going to use calculus in real life?" Because I know how useful they really are.
What math textbook is that? I’d find it useful to study from.
@@theeviloverlord7168 HSC 12th: Mathematics and Statistics: Part 2
"round gravity to 10 as always" haha
You should check out Sean' Carroll's Biggest Ideas In The Universe. He sets c (speed of light) and h-bar (reduced planck constant) to 1 to simplify the math. It's just the way science and math works best.
@@kindlin Will do 😃 thanks!
@@kindlin not the same thing, rounding g is an approximation, setting the constants to 1 is not because you consider different variables. For example, setting c to 1 could mean that the time you are using afterwards is a different time (where the unit is not one sec). Nothing to do with the approximation of g, in which case you just accept to have slightly different result (or maybe the precision of the other datas you are using is so bad that it would be sensless to use a more precise g)
@@francescocitterio54
Setting it to 1 or 10 is similar enough. The mathematical reason for doing this is the exact same, to simplify math. 1 is just much simpler. You could set G=1 and do other weird things with the math unrelated to we're talking about here (but similar to what Sean does).
Ok
Damn I wish more people understood just how mind blowing physics and Calculus really are. Like these equations describe the damn universe, the universe itself runs on mathematics and physics. Mathematics is literally God's language and it's so beautiful.
You are the man Daluved "1"
More likely the mathematics is reflecting our way to cope with complex ideas and to structure them.
The universe isn't run by mathematics, it is our language that we use to understand how the universe works
God is just an illusion.
@@vv8104 perhaps
Former engineer, now a nurse, no matter how much I gorge my brain on new medical terminology, biology and pharmacology, I always find myself coming back to the topic of STEM. I wish I could go back to engineering but the jobs just aren’t there, everyone only wants to hire for short term projects.
Do you think about Medical Dosimetrist or Nuclear Medicine Tech…good money and you applied math and physics….
What country do you live in?
Did my master's thesis on a differential equation, loved your breakdown!
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.kqmb
What equation was it about?
Mann I was just solving differential equations when this video popped up!
Liar.
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.mkqj
It has been many decades since I first learned various methods for solving differential equations, and used them throughout my career as an engineer. I remain impressed about how easy it is to write down a differential equation, as opposed to the difficulty in solving it.
Despite advanced methods of numerical analyses, analytical solutions still come down to educated guesswork: intuit a possible solution, plug it into the equation, and find out if it works.
You have a teaching gift, thanks for putting this together. Subbed.
It's wierd that in schools we are taught to solve them by just learning the formulas and getting the right answers and not the practical usage. It would have been easier to learn about them by having them connected to some practical usage.
Like what
@@DairangerSentai7 like you see in the video
Maybe you were one of those people sleeping or picking your nose at the back of the class then, because they definitely mentioned it to my class.
@@Michael-mh2tw In a post-secondary, or like high-school? My high-school teachers never talked about applications, and yeah I did actually listen to the lesson
@@soupy5890 no one was talking to you.
I consider Differential eqn as a branch of mathematics (actually Calculus) which are very intresting and very helpful in every day life.Btw thx for this video! Good luck!
Why you don't see this
ua-cam.com/video/RWz78wPMeEg/v-deo.html
Consider doing a episode on Integral Equations.
These seem to get overlooked in the typical "Math Methods" course, but then are used extensively in Graduate Level Physics, "Jackson", etc.
For pursuit curves, if you do not know the trajectory of the pursued object/person/variable, you can use a Kalman filter or polynomial regression to predict it, then apply the pursuit algorithm...
Great video! it's always nice to see real world applications for DEq. I believe that's when the "ah ha" moment happens. The chain with the barbell equation was one i used when i worked at the U of Tampa Human Performance Lab.
I wish i had a maths teacher like him
Instead of just blindly solving the equations by formula, we know how to imagine & understand
During my time at school... Something which you can't perform outright seemed boring...but now watching yt videos getting context of what is the actual application of these equation is really fascinating...Applications were there in the textbooks but we're not at all relatable as those were some mumbo jumbo high level experiments...
I am just gonna start teaching professionally and this is pure gold to make students interested. Thank you so much.
I was reading about Image segmentation there we have to segment one image to another. And this is the foundation. Amazed!!
How do I get girls to like me?
Differential equations
How do I get this stain out of my pants?
Differential equations
What happens if I can't solve a differential equation?
Try different differential equations
That's right folks they do it all. They can slice and they can dice, make your teeth whiter, and your car go faster. and all for the low low... ok im done.
when u can't solve des that's where python is ur friend.
No opposites-- aren't different, but ops-- face in Egyptian. APS-- Hawaiian for, what's the problem here, etc...
@@azmanmatamin9020 Kinda crazy you should ask that since your name is the same as my ex's cat and she did, that's who. I was also sad when pus pus died. 😿
Differential equations put a white stain on my pants 😳
How do I get girls to like me using differential equations?
Just finished calc 3 and linear algebra and I can finally understand math that they do in UA-cam videos
I just finished algebra ii, and yet I still completely understand the first ten minutes (except for some of the math around 8 minutes) of the video. So brilliantly explained! Thanks.
I guess one brilliant description for this amazing teaching/explanation is BRILLIANT!
Really nice video! Makes me miss teaching DEs... I wish we didn't focus so much on analytic solutions, but elementary is elementary. I wish there was more money in physics based solvers, I would love to find a job where I can build physics-based models like I did back in school...
"I don't care I'm going to economics"
Macro & interest growth differential equations(and friends): *"allow us to introduce ourselves"*
Edit: highlighted the irony more clearly
You will still use it economics for various graphs and other stuff like population growth
Economics is full of differential equations
@@arnaldo8681 i know lol, I was parodying the irony of those who take economics because it's 'easy'/'mundane'/'everyone can do it', yet still meet differential equations anyway...
Btw, in macro, or micro as well?
@@revimfadli4666 its mostly in macro, but you can find them in micro as well. In mechanism design, for example, sometimes they show up
en.m.wikipedia.org/wiki/Mechanism_design
@@arnaldo8681 wow thanks!
Wow! You actually made me excited about differential equations. Great job!!!
Fascinating video. Thanks for your hard work!
Differential Equations: *everything*
Literally every student: *confused screaming*
See this man
ua-cam.com/video/RWz78wPMeEg/v-deo.html
Differential equations are easy enough just wait till you get to partial differential equations
@@mastershooter64 complex analysis
@@mastershooter64 wait till you get something that isn't addition and subtraction
2:40 OMG I love that show. I wish there were more math related shows
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.bfsz
man, I love your videos, your voice and your vibe... you are amazing!!
Thank you so much, really great video, knowing why you do something is a must to learn something, generations of students have grown up not knowing why they learned something so gave it little effort,
Nobody:
Me: I have differential equations test in 2 hours, I think I'll watch this video right now.
How was it
Oh, I did it actually pretty good I think, Hamiltonian equations are kind of pretty and easy to handle. Thanks!
@@t.e.fcastle1069 gj
I know how to differentiate but have never done work with differential equations like these :/
Zach star and 3B1B .
Perfect!
See this man
ua-cam.com/video/RWz78wPMeEg/v-deo.html
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.qjho
Thanks for such a wonderful and awesome set induction about differential equation.
your efforts are easily visible through your eyes. great work
Haha, Zach you just had to round up gravity. LMAO!
It's the engineer in him
Round up? How do you round up from 10? ¯\_(ツ)_/¯
👍🏻 I’m perpetuating the engineering joke 😁
Because 10 has a round in the form of zero
@@_instanze_ NOOO! In civil engineering: "We don't do that here"
I got a B+ in differential equations this semester. It was super easy, I really enjoyed it!
Amazing! Great job, loved it
Amazingly explained, congrats!
Hi zach !Lots of engineering topic are taught without giving any inituation /application. .. I believe step by step you will cover whole engineering course and would be able to create new engineering course 😅 best of Luck. ..greetings from India
Are you preparing for JEE Advance?
@@Stabokb I am engineering passout of 2015
See this man
ua-cam.com/video/RWz78wPMeEg/v-deo.html
jaikumar848 which university did you go ?
@@jaikumar848 B.Tech from IIT Madras.you?
My signals and systems course is like a kick in the face that says "hey man! Heres why you shouldve payed attention in DE!"
Suddenly this came to my recommendation!!!
I m a biology lad but your video has increased my interest in maths now!!
Thank you for this video. I opted out of calculus in college and always regretted it and this is the first video I’ve found that explains what differentia equations are used for without assuming the viewer already knows a ton of calculus-specific vocabulary. Thanks for helping me understand how they work a little better.
17:28 , for a moment i thought he said : "If you wanna die" .. he got me excited
Dive lol
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.vknj
I learned these a year ago and went through hell to pass the class and I’ve forgotten them all.
SAME HAHAHA
I learned this a year ago as well, and id Ace any first level calculus test. Your situation should not be normal
@@abdallababikir4473 to be fair i was never really interested in it, and i just studied just enough to pass so 🤷♀️🤷♀️ it'd be normal
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.enrv
Best video i watched this year। Thankyou for such videos, they inspires us towards science since we come to know why we learn all these and where we will be implementing them in future.
Right on. Thanks for sharing.
Man if I had the same passion watching this video when I barely passed Maths.
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.miyg
Up until Calc2, I had been a natural in math. But it stopped clicking sometime around when we were studying integrals, logarithms, and series. The nail in the coffin was the project I chose to try, which was to describe the curve of an archery bow as it was being drawn, relating the bow length, arc, and draw length or something like that. I flunked that project. I've since looked it up and found that I had bitten off more than I could chew because the related math and physics were a bit beyond what I had been studying at the time. But I didn't know that because my teacher didn't preview our project ideas to make sure we were on topic. So that's my advice to any would-be teachers reading. Be proactive with your students, ask them for updates on their semester projects and ask if they need any help. Don't just throw them in the deep end with no support.
Interesting presentation. Great explaination. Helps to clear the mind
thank you so much. I was about to start differential equation and i needed this. ALSO we have this chapter called pair pf straight line, i cannot relate that at all to any real life situation and even though i have memorized the formulas but i cannot imagine anything at all
I tried solving my own version of your equation at 2:15, but with the area = the square of the arclength. It got very messy, ended up with a very nonlinear second order diff eq that looks hard to even numerically solve. I wish more diff eq's were easy to solve analytically.
Universe: BOOM! Here's a bunch of stuff.
Us: Cool, how's it all work?
Universe: BOOM! Here's Differential equations.
Me: Cool, solve mine too.
See here man
ua-cam.com/video/RWz78wPMeEg/v-deo.html
It reminds me of the *_dark water in this video_* ua-cam.com/video/Tl5oHZrIZo0/v-deo.html&.svjx
This is what I needed in my whole 12th for intuition . Thanks
i saw this at the end of my requirements list after calc 3 and wondered what could be more difficult than calc 3...
thank you for scaring me.
what is the dot product of velocity and position vectors?
I got into this stuff to do fluid simulations in my computer graphics courses. This video is very informative as far as the applications go. For sure made by an engineer ahaha
I find it satisfying and scary at the same time.
Thinking of the time and energy I have to put in to really understand the concept scares me.
Thanks for the video. It was educating and relieving.
Thanks for the Video, great job
This far too detailed and advanced for my secondary school brain
Respect Sir Isaac Newton
Thank yous for sharing, Appreciate your tutorial and explainations
OMG The pursuit curves were freaking awesome!
I'm really curious where something like an exact or almost exact diffyq comes into physics. Is that not a thing?
Linear diff eqs are used for solving feedback controller gains. Just representing f=ma or t=j*theta as differential functions of joint position or linear position. Converting them to the frequency domain, you can tune the curve response shape by placing poles with pid gains. The conversion to the time domain is based on Euler’s formula where the time response can be represented as exponential sins and cosines. The weirder version of this stuff is state space control where you actually control each derivative of the diffeq
These are all time derivatives however
@@jimmyhoffmann4950 that sounds a lot like Fourier analysis. I was specifically asking about exact diffyqs. I'm not sure if that's what you're getting at
@@carmangreenway huh yeah never heard of those before, should’ve looked it up before I responded. Yeah I’m talking about the Fourier transform
@@carmangreenway lol I actually remember those from a math class I took last year. I have no knowledge of there practical application, but it was an engineering math course so there probably is
At 1:46 meaning of the differetial equation was unexpected! ! Thanks for that!!
awesome! I like the applications, gives me a sense of all that what's happening with diff. eqs.
Nicely explained! Thanks