Lecture 1: The Geometrical View of y'= f(x,y) Lecture 2: Euler's Numerical Method for y'=f(x,y) Lecture 3: Solving First-order Linear ODEs Lecture 4: First-order Substitution Methods Lecture 5: First-order Autonomous ODEs Lecture 6: Complex Numbers and Complex Exponentials Lecture 7: First-order Linear with Constant Coefficients Lecture 8: Continuation Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients Lecture 10: Continuation: Complex Characteristic Roots Lecture 11: Theory of General Second-order Linear Homogeneous ODEs Lecture 12: Continuation: General Theory for Inhomogeneous ODEs Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs Lecture 14: Interpretation of the Exceptional Case: Resonance Lecture 15: Introduction to Fourier Series Lecture 16: Continuation: More General Periods Lecture 17: Finding Particular Solutions via Fourier Series Lecture 18: 18.03 Differential Equations, Lecture with Prof. Haynes Miller and Prof. Kim Vandiver, Spring 2010. Lecture 19: Introduction to the Laplace Transform Lecture 20: Derivative Formulas Lecture 21: Convolution Formula Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs Lecture 23: Use with Impulse Inputs Lecture 24: Introduction to First-order Systems of ODEs Lecture 25: Homogeneous Linear Systems with Constant Coefficients Lecture 26: Continuation: Repeated Real Eigenvalues Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients Lecture 28: Matrix Methods for Inhomogeneous Systems Lecture 29: Matrix Exponentials Lecture 30: Decoupling Linear Systems with Constant Coefficients Lecture 31: Non-linear Autonomous Systems Lecture 32: Limit Cycles Lecture 33: Relation Between Non-linear Systems and First-order ODEs
I got nostalgic and came back here to see this dude. His lectures were supplementary material for my DE class and I remember watching these videos all the time in 2018. Just looked it and up and he passed away in 2021, but his lectures are going to continue teaching so many.
This is amazing: this is the only guy on the entire Internet who says "let's get started" at the start. Most people don't say it until about ten minutes in.
Ken Ya Ken, I was pretty impressed all around. I don't think it's so much tedious as *tough*, and this guy gives me some faith that I might be able to get through it this time. I thought that not fucking around with the "let's get started" being a meaningless formula, but actually meaning it, like he's getting started, ws a good sign, and he actually carries through pretty well, I thought. Your mileage may vary: my theory is that differential equations are ike languages. I wish I'd learned them a whole lot earlier. It's so much easier before about your seventh birthday! :-) -dlj.
Ken Ya Ken, (Later) Looking around I see there a set of TH-cams for this same course, 18.03, in 2011, and another one that may be interesting, I don't know yet, 18.09, "Eigenvectors and Eigenvalues" in 2011. This last one is slugged as Linear Algebra in some places but on the first page of the course it talks a bit about differential equations. Anyway, over the long haul I need all of Linear, all of Eigen, and all of Differential, But you might want to check out the availables. Let me know what you think. -dlj.
sebastianzx6r Sebastian, I imagine it's mostly nervousness. They're partly impressed by what a wonderful thing it is to be "on TV" and nervous about being exposed to people they can't tell to shut up or glare at. This guy just knows his stuff, and goes ahead and teaches it. Cheers, -dlj.
I took differential equations (this course, 18.03) with Arthur Mattuck in 1980. He was one of the best teachers at MIT in my opinion. Also, Gilbert Strang who taught linear algebra (18.06) was excellent, one of the best, clear, lucid presentation of concepts and material.
I agree. I took both in 1977. I also took 18.711 (Game Theory) from Professor Strang in Fall 1977. The numbering of the class dates back to when Nash was at MIT, a take on 7 and 11 in the game of craps.
The only thing I can say is thanks a million, million, million..... Professor Mattuck and MIT. I did not have differential equations course in college. I learned it from these lectures. Great teaching!
hahaha , we gotta make protests to force them to put one! :D .. Seriously, I've never seen anyone teaches these incredible stuff about ODE's. It's really worthy to be in HD Quality.
coobityou young whippersnappers and High definition, back in my day we were lucky if the writing was legible in videos and would have have killed for 240p. young people today have no idea how good they have it, sigh
I loved this lecture like no other in a long time ago. The Professor transmits confidence in the subject which encourages you to pay attention and learn. Great work!
Heinrich Dorfmann The source videos were actually recorded with decent quality. It is the compression that is potato-like. Videos produced before 2007 were quarter screen (320x240) Real Media files. All videos produced after 2007 are at least standard definition or greater. We have a number of old videos that have been recently produced/remastered-old videos with good quality-but this is not one of them.
Andrew Quinn Sadly much of the early editing work was not saved. Depending on what is available (tapes, DVDs), we digitize what we can find and then edit them. We try to clean them up as best we can- color balancing, brightness/contrast, noise reduction, etc. In this particular case, these videos were recorded on tape.
Re: Questions about HD video: All videos published before 2007 were originally quarter screen Real Media files. No edited masters were saved. To make these higher quality would require us to re-edit them. We currently prioritize new videos over old, so these will probably not be re-edited anytime soon.
I'd rather watch a good lecture in low def than a bad one in HD. Thanks for putting them up and please don't hesitate to put up more of these old (I'd prefer to call them 'classic') lectures.
My mind is Fucking BLOWN! I am from India and all I've ever been taught was how to solve differential equations Algebraically..and just memorize formulae... But the Geometric Interpretation is so beautiful 🥺
I love math. Is it weird I watch these videos for fun? I'm an engineer and math was my most favorite. Having to take many math classes, this guy is a good math professor.
Thank you for this MIT! Im taking an ODE class right now and my professor is so terrible. If not for OCW and this series, I would definitely be struggling hard.
Just finished this course. I have had the opportunity to view all the MIT math courses - they are excellent, but this one stands out. Prof Mattuck is...well...brilliant. I may even buy his book if I can find the right price. Thank you MIT.
Most kids that go to MIT have taken AP courses where they could be freshmen when they take this class. I took it as a jr and i ended up dropping. My mind couldn't handle it.
This is a fantastic lecture on Direction Fields and Integral Curves in Differential Equations. This is a great way to introduce Differential Equations to all students
Tnx prof mattuck & MIT for such "high standard" educational resources for "free" and for making such possibility to be learning while you're thousand miles away 🙏 Besides today i find out about prof mattuck and I can't say how heart broken i got. It's so fascinating that one could have influence others even after his/her death Rest in peace 🕊️ prof mattuck ❤
Many accredited schools have you study : separable and linear dif eqs with slope fields and eulers numerical method during your last semester in Gr. 12 though only very briefly , in our book all that was covered in 4 pages
High School level Calculus is taught every where in the world, my friend. Do not confuse Differential Equations with Differential Calculus (the one you learned at HS). I can see you have no idea what ODEs are.
@@gvcallen I can see I wrote this comment 11 years ago. If you want to know what's this about go ahead and read the other posts. What do you care anyway?
@@DrPG199 this comment is directly on the video and not in a sub-comment thread, making it seem like you were talking to the lecturer, which was very confusing for me. Obviously you were not haha
In math 9 times on 10 if you don't understand the problem is not you but the teacher and this is a good example about the excellence in teaching math. Tank's to You Tube we can learn excellent math from excellent mathematician..
simply the fact that you can pause and take proper notes, then press play again, makes online courses so much more advantageous, if you like to take your time like i do at least
Wow. Loved this one. He's actually teaching the important concepts out of the BAT. Showing them the Forest before getting inside the trees and going into the leaves.
This is the beginning of the future of University education. If every professorial lecture was available free to everyone, the entire degree system will have to be revised. I think this is a good thing. No one should be able to own knowledge. It should be available for free for everyone and we shouldn't have to purchase a degree to be qualified for a job. Self-education can be sufficient if one applies themselves. Thumbs up if you want college to be free!
@ProfitMuhammed Think before you type. This is calculus 4. They have differential equations in all types of subjects, and a whole chapter in second semester single variable calculus (calculus 2). This class, differential equations, is not in high school. This is MIT, meaning one of the best, if not the best, technology/science schools on the planet.
Wow I learned differential equations in college, but I had to study for hours because the teacher couldn't teach, but this guy is good teacher, very easy to understand.
Summary: In this video the professor doesn't solve any differential equations using analytical methods, rather, the focus of this class is the geometrical representation of 1st order ODEs using the method of direction fields and integral curve sketching Although it might sound that this class is redundant for people looking to solve 1st order ODEs analytically but it's worth watching as it provides a new way to look at ODEs and their behavior
Due to covid I'm taking ODE online, and my prof does not do lectures, just tells us to read the book and posts PowerPoints. Thank you Dr. Arthur Mattuck, you are a life saver, and thank you MIT Opencourseware for providing these videos for all of us struggling students.
(Pausing at 01:00) I don't get it. The course says "Differential Equations" and he starts by saying "I assume you all know what differential equations are". If that's what he assumes, what are the 33 lectures for?
stevenvh17 in the first course of calculus, you have to work with separable differential equations. He's just saying that you should have a general idea is to what differential equations are.
please do. Nobody asks for you to make this "stuff", nobody waits for you either. This teacher is great, nomatter the sign, he explains very well. I must say it's the first time I hear about it, after more than 5 years after high school, that's France.
I cannot thank MIT for doing this. And I wish I had a porf Like Dr. Mattuck the first time I took differential equations a decade ago. I learnt (and assimiliated) more from this one video than I learned from that entire course possibly,a t least what I I retain from that class.
For a vigorous purpose, you have to note that ONLY some continuous functions HAVE DERIVATIVES. But in most cases, yes, you have derivatives(especially for elementary functions).
Elim Lacy you mean like college algebra trig sins cosines conics matrices composition functions etc? I'm doing it now scrunched into a 4 wk course we still have a while before we get to this bro u gotta do calc 1,2 and 3 first you did ur precal in one class though? My school divided it into college algebra and college trig.
John Cooley Well to think of it. Pre cal wasnt much of anything but a huge review of algebra and trigonometry. And there was some minor things extra like. Conioncs.... Im guessing conics is precalculus because conics is clearly the fundamental shapes that make up everything as we see it. That must be a huge headace cause that math is alota info. Good luck broski - john cooley
abdalrahman mahdly : couldn't find most of them either, but managed to find the 33. Here it is man => ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-33-relation-between-non-linear-systems-and-first-order-odes/ Good luck with it. Cheers.
Abdulrahman Mahdaly Lectures 18, 34, and 35 are not available. Sometimes this is due to IP reasons, sometimes due to technical reasons (no audio or bad audio), and sometime because the lectures were not recorded. The reasons for missing 18, 34, and 35 are not given.
+effortless35 According to the course calendar: lecture 18 topic was "Engineering applications", lecture 34 topic was "Complex or repeated eigenvalues Eigenvalues vs coefficients", and the topics for lecture 35 were "Qualitative behavior of linear systems; phase plane". For more information see the course on MIT OpenCourseWare at: ocw.mit.edu/18-03S06
ODE's (ordinary differential equations) are not only useful, but often indispensable, in modeling a wide variety of physical problems. The essence of an DE is that it involves at least one derivative(i.e. one rate of change). If you are trying to develop a model that explains and predicts changes in population dynamics, for example, you must be able to account for growth rates (i.e. rates of change), and so you need DEs. In addition to physical problems, they are also important in economics.
c++ ? i + b = c c + i = c1 c + b = c2 c + c1 = c3 c + c2 = c4 c4 + b = i++ int i = 54 int b= 2 int c = 666 shoot C++ is the best way for me to learn this kinda math, most people know this stuff they just can't put the symbols to common sense. C++ makes it easy in my opinion. I would say line element math would come in handy for designing turbo fins for rocket engines, heat emission, and wind tunnel testing.
Fair enough. There are a few good reasons to do history, I was just thinking in most cases, history is something best studied in one's own private time. Especially in the UK, if you're a man studying history, don't expect to earn much, if anything, more than you would if you went straight into work.
Peter Jackson I’m only in my first year so I have plenty of time to change it too, but i’m just stuck because nothing else interests me and I don’t really have a passion for anything else. History excites me, so I figured why not teach if
finally, I now can travel through time. Thx youtube AI, i promise you to see your older version in 1849 and i will make you smarter for my future search preferences.
@dearchiv "Cline" is a root word meaning slope as in incline, decline, or recline. To my knowledge, isoslope is not used as a synonym for isocline very widely, if at all, and all of the textbooks I've surveyed mention isoclines when referring to the method described in this lecture.
Awesome! I'm taking Elementary Ordinary and Partial Differential Equations in the Fall, I've been following the book the video lectures are going to be an amazing help! Thanks MIT for the free content.
Pretty good Professor. I learned more from this video than I have the past three weeks at my college, I'm having trouble understanding my professor. This really brings better insight unto what I have been reading in my text book. Thanks MIT !
Lecture 1: The Geometrical View of y'= f(x,y)
Lecture 2: Euler's Numerical Method for y'=f(x,y)
Lecture 3: Solving First-order Linear ODEs
Lecture 4: First-order Substitution Methods
Lecture 5: First-order Autonomous ODEs
Lecture 6: Complex Numbers and Complex Exponentials
Lecture 7: First-order Linear with Constant Coefficients
Lecture 8: Continuation
Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients
Lecture 10: Continuation: Complex Characteristic Roots
Lecture 11: Theory of General Second-order Linear Homogeneous ODEs
Lecture 12: Continuation: General Theory for Inhomogeneous ODEs
Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs
Lecture 14: Interpretation of the Exceptional Case: Resonance
Lecture 15: Introduction to Fourier Series
Lecture 16: Continuation: More General Periods
Lecture 17: Finding Particular Solutions via Fourier Series
Lecture 18: 18.03 Differential Equations, Lecture with Prof. Haynes Miller and Prof. Kim Vandiver, Spring 2010.
Lecture 19: Introduction to the Laplace Transform
Lecture 20: Derivative Formulas
Lecture 21: Convolution Formula
Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs
Lecture 23: Use with Impulse Inputs
Lecture 24: Introduction to First-order Systems of ODEs
Lecture 25: Homogeneous Linear Systems with Constant Coefficients
Lecture 26: Continuation: Repeated Real Eigenvalues
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
Lecture 28: Matrix Methods for Inhomogeneous Systems
Lecture 29: Matrix Exponentials
Lecture 30: Decoupling Linear Systems with Constant Coefficients
Lecture 31: Non-linear Autonomous Systems
Lecture 32: Limit Cycles
Lecture 33: Relation Between Non-linear Systems and First-order ODEs
thank you so much!
king👑
: V
Rest in peace professor. You will never be forgotten. Your contributions to education and mathematics will be remembered forever.
This man is the greatest consumer of chalk in the 21st century
muse5381 lol
Mike haha so thick and bold
For good purpose
Ha ha ha ha.
Mike - that was too damn funny!!!
I got nostalgic and came back here to see this dude. His lectures were supplementary material for my DE class and I remember watching these videos all the time in 2018. Just looked it and up and he passed away in 2021, but his lectures are going to continue teaching so many.
This is amazing: this is the only guy on the entire Internet who says "let's get started" at the start. Most people don't say it until about ten minutes in.
Ken Ya
Ken,
I was pretty impressed all around. I don't think it's so much tedious as *tough*, and this guy gives me some faith that I might be able to get through it this time.
I thought that not fucking around with the "let's get started" being a meaningless formula, but actually meaning it, like he's getting started, ws a good sign, and he actually carries through pretty well, I thought.
Your mileage may vary: my theory is that differential equations are ike languages. I wish I'd learned them a whole lot earlier. It's so much easier before about your seventh birthday!
:-)
-dlj.
Ken Ya
Ken,
(Later) Looking around I see there a set of TH-cams for this same course, 18.03, in 2011, and another one that may be interesting, I don't know yet, 18.09, "Eigenvectors and Eigenvalues" in 2011.
This last one is slugged as Linear Algebra in some places but on the first page of the course it talks a bit about differential equations.
Anyway, over the long haul I need all of Linear, all of Eigen, and all of Differential, But you might want to check out the availables. Let me know what you think.
-dlj.
Yep, I've been watching other videos and the guys ramble for 20 minutes then finally start up.
sebastianzx6r
Sebastian, I imagine it's mostly nervousness. They're partly impressed by what a wonderful thing it is to be "on TV" and nervous about being exposed to people they can't tell to shut up or glare at.
This guy just knows his stuff, and goes ahead and teaches it.
Cheers,
-dlj.
Just like every vlogger. lol
Given the video quality I'm grateful that he writes so large.
I took differential equations (this course, 18.03) with Arthur Mattuck in 1980. He was one of the best teachers at MIT in my opinion. Also, Gilbert Strang who taught linear algebra (18.06) was excellent, one of the best, clear, lucid presentation of concepts and material.
I agree. I took both in 1977. I also took 18.711 (Game Theory) from Professor Strang in Fall 1977. The numbering of the class dates back to when Nash was at MIT, a take on 7 and 11 in the game of craps.
@@stephenj.bridges8038 what do you do now sir ?
The only thing I can say is thanks a million, million, million..... Professor Mattuck and MIT. I did not have differential equations course in college. I learned it from these lectures. Great teaching!
which book he is talking about?
@@feynmath Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 6th ed.
For Newton's sake, please put some HD version of this lecture!
hahaha , we gotta make protests to force them to put one! :D .. Seriously, I've never seen anyone teaches these incredible stuff about ODE's. It's really worthy to be in HD Quality.
coobityou young whippersnappers and High definition, back in my day we were lucky if the writing was legible in videos and would have have killed for 240p.
young people today have no idea how good they have it, sigh
I guess, back in your days the road to school was in a non-conservative gravitational field: To school and From school were both uphill walks :)
+coobit bwahahaha, comment of the year goes to you kind sir. :)
.
i dont know how i got here
im scared
You should be. Diff Eq is very hard
pikapiku why?
Fate.
@@ImGriffinP No, you just suck at math
It's not because of the math. This teacher is really really fucking bad at teaching.
I loved this lecture like no other in a long time ago. The Professor transmits confidence in the subject which encourages you to pay attention and learn. Great work!
MIT, filming with only the finest potato money can buy.~
Joseph Heavner
there are mit lectures from 1968 that are better quality than this
Heinrich Dorfmann
The source videos were actually recorded with decent quality. It is the compression that is potato-like. Videos produced before 2007 were quarter screen (320x240) Real Media files. All videos produced after 2007 are at least standard definition or greater. We have a number of old videos that have been recently produced/remastered-old videos with good quality-but this is not one of them.
*****
So wait, how do you guys go about remastering the source videos then? Were they recorded on tape?
Andrew Quinn
Sadly much of the early editing work was not saved. Depending on what is available (tapes, DVDs), we digitize what we can find and then edit them. We try to clean them up as best we can- color balancing, brightness/contrast, noise reduction, etc. In this particular case, these videos were recorded on tape.
***** Would it be particularly difficult for you to do a modern course on differential equations...
Re: Questions about HD video:
All videos published before 2007 were originally quarter screen Real Media files. No edited masters were saved. To make these higher quality would require us to re-edit them. We currently prioritize new videos over old, so these will probably not be re-edited anytime soon.
Spoiled brats. This was eminently watchable. Thank you for putting it up.
I'd rather watch a good lecture in low def than a bad one in HD. Thanks for putting them up and please don't hesitate to put up more of these old (I'd prefer to call them 'classic') lectures.
FAIL
So, will the newer lectures be uploaded soon?
This lecture is from 2003. Spring 2006 above must refer to something else. I took this class in Spring 1977!
240p, we meet again.
I was three years old when this was recorded. Awesome that I get to benefit from this 21 years later.
My mind is Fucking BLOWN! I am from India and all I've ever been taught was how to solve differential equations Algebraically..and just memorize formulae...
But the Geometric Interpretation is so beautiful 🥺
I love math. Is it weird I watch these videos for fun? I'm an engineer and math was my most favorite. Having to take many math classes, this guy is a good math professor.
I do the same,, watching it just for fun. Love professor Mattuck
Then why are you an engineer? Be a physics or maths student. You will get to learn even more.
@@maxwellsequation4887 money
Thank you for this MIT! Im taking an ODE class right now and my professor is so terrible. If not for OCW and this series, I would definitely be struggling hard.
Just finished this course. I have had the opportunity to view all the MIT math courses - they are excellent, but this one stands out. Prof Mattuck is...well...brilliant. I may even buy his book if I can find the right price. Thank you MIT.
We will miss you dearly Sir
Yes😣😣😳😳
this professor is very clear and intuitive (except the video quality , not his fault, isnt great)
This guy is pretty cool but I feel like I'd be intimidated by him if I were a freshman taking his class
It's all in how you look at it. It seems much more difficult than it appears.
Dif eq isnt a freshman level class
@@indianafishing Well, I think that now, it can be, though that's not always the standard
@@indianafishing Might be a bit late, but empirically there are plenty of freshman taking this class here.
Most kids that go to MIT have taken AP courses where they could be freshmen when they take this class. I took it as a jr and i ended up dropping. My mind couldn't handle it.
a huge thanks to all you guys at MIT, seriously, this stuff really helps with revision or just seeing the material taught by someone else
5*
its a shame that these fine lectures are not in fine video quality
at the end: *drops the chalk like how a rapper drops the mic
LMAO
@14:06 2003!!!!!!!!!!!! I WAS 1 YEAR OLD BACK THEN!!!!! Thank goodness the internet exists so even I can benefit from these videos!!!
This is a fantastic lecture on Direction Fields and Integral Curves in Differential Equations. This is a great way to introduce Differential Equations to all students
Tnx prof mattuck & MIT for such "high standard" educational resources for "free" and for making such possibility to be learning while you're thousand miles away 🙏
Besides today i find out about prof mattuck and I can't say how heart broken i got.
It's so fascinating that one could have influence others even after his/her death
Rest in peace 🕊️ prof mattuck ❤
Hello my name is Fernando Nora
I'm traslating those lectures to spanish language.
How could I contact with you in order to give you my traslations?
Thanks for offering! Contact us through our feedback form at ocw.mit.edu/jsp/feedback.jsp and we'll get back to you about your translations.
que grande, capo total!
Asombroso!!!!
Gracias por aportar!!!
Increíble! esperando donde obtener los videos subtitulados en español! buen trabajo!
que agradable sujeto
Damn, people take diffiq in high school!? When I went to high school, if you took precalc you were smart.
airbornerecon11
Most in my school take AP Calc AB/BC
Some take Diff EQ/Calc III
airbornerecon11 you do separable dif eqs in calc classes sometimes
He wasn't talking about your kind of high school lol
airbornerecon11 Mine only had Calc 1... 😠
Many accredited schools have you study : separable and linear dif eqs with slope fields and eulers numerical method during your last semester in Gr. 12 though only very briefly , in our book all that was covered in 4 pages
Lec 01. Direction field (Geometric analysis)
Lec 02. Numeric solutions & Euler Method
Lec 03.1st Order Linear ODEs, integral factor
Lec 04. Substitution (homogeneous, Bernoulli)
Lec 05. Autonomous systems
Lec 06. Complex Numbers (review)
Lec 07. 1st Order Linear Const Coeff Diff Eq with sinusoidal input
Lec 08. 1st Order Linear Const coeff Diff Eq with sinusoidal input
Lec 09. Homogeneous, 2nd Order Linear Const Coeff Diff Eq, characteristics Eq
Lec 10. Homogeneous, 2nd Order Linear Const Coeff Diff Eq, "under damped" case
Lec 11. existence & uniqueness theorem
Lec 12. Inhomogeneous, 2nd Order ODEs
Lec 13. particular solutions (D Operator Method)
Lec 14. Resonance 1
Lec 15. Fourier series
Lec 16. Fourier series
Lec 17. resonance 2 (Fourier series point of view)
Lec 19. Laplace transform
Lec 20. Laplace inverse
Lec 21. Laplace transform, convolution
Lec 22. Laplace transform (continue)
Lec 23. Laplace transform (continue)
Lec 24. Systems of ODE
Lec 25. Homogeneous systems
Lec 26. eigenvalues & eigenvectors
Lec 27. Systems of ODE, types of solutions
Lec 28. Fundamental Matrix, inhomogeneous systems, variation of parameters Method
Lec 29. Exponential Matrix
Lec 30. Decoupling & Decoupled systems
Lec 31. Nonlinear systems
Lec 32. Limit cycles
Lec 33. Volterra's problem
RIP, your legend will never die. Thank you forever!
good job, David Letterman.
High School level Calculus is taught every where in the world, my friend. Do not confuse Differential Equations with Differential Calculus (the one you learned at HS). I can see you have no idea what ODEs are.
What are you on about lol?
@@gvcallen I can see I wrote this comment 11 years ago. If you want to know what's this about go ahead and read the other posts. What do you care anyway?
@@DrPG199 this comment is directly on the video and not in a sub-comment thread, making it seem like you were talking to the lecturer, which was very confusing for me. Obviously you were not haha
@@gvcallen TH-cam Comments 11 years ago were different, funny how this thread started up again as I clicked on the video.
@@MrDroenix Yeah realized that now haha. Funny indeed
In math 9 times on 10 if you don't understand the problem is not you but the teacher and this is a good example about the excellence in teaching math. Tank's to You Tube we can learn excellent math from excellent mathematician..
simply the fact that you can pause and take proper notes, then press play again, makes online courses so much more advantageous, if you like to take your time like i do at least
damn his lecture is so good it takes away my attention from the matter :).
39:14 1=1, bless those wise words!
After series of studies and proofs I have discovered that not only 1=1 but that 2=2 also! Can you imagine? And does 3=3? We have to find out.
Wow. Loved this one. He's actually teaching the important concepts out of the BAT. Showing them the Forest before getting inside the trees and going into the leaves.
This is a great fortune to get these lectures by MIT Professors.
i wish we could at least get 720 quality video here. 240 is pretty difficult to make out what's on the board.
You get all the value for $0, your thoughts should not even drift into complaining!
^ complaints not allowed
it was shot in 2006
+Keshav Kasat 720 was introduced in the United States in 1998
Keshav Kasat 2003*
thank you professor Arthur Mattock.
i have a dream one day i will be MIT professor...but
problem is am from sub-saran Africa...bless u man
I love the way of teaching he had a tremendous skill of teaching thanking MIT for this masterpiece
Happy Birthday Professor Mattuck!
Thank you for these wonderful lectures.
hocam allah sizden razi olsun sayenizde guvenlikci olarak ise girdim
i aint going to school tomorrow
I ain't going to the boston marathon tomorrow
Sir Craigie 😀
This being 2003, mostly computers draw them for you
This is the beginning of the future of University education. If every professorial lecture was available free to everyone, the entire degree system will have to be revised. I think this is a good thing. No one should be able to own knowledge. It should be available for free for everyone and we shouldn't have to purchase a degree to be qualified for a job. Self-education can be sufficient if one applies themselves. Thumbs up if you want college to be free!
@ProfitMuhammed Think before you type. This is calculus 4. They have differential equations in all types of subjects, and a whole chapter in second semester single variable calculus (calculus 2). This class, differential equations, is not in high school. This is MIT, meaning one of the best, if not the best, technology/science schools on the planet.
I thought he was being sarcastic when he said some took this in high school
Haha I'm taking it right now... slope fields... help
Civilized people use Leibniz notation.
Wow I learned differential equations in college, but I had to study for hours because the teacher couldn't teach, but this guy is good teacher, very easy to understand.
Summary: In this video the professor doesn't solve any differential equations using analytical methods, rather, the focus of this class is the geometrical representation of 1st order ODEs using the method of direction fields and integral curve sketching
Although it might sound that this class is redundant for people looking to solve 1st order ODEs analytically but it's worth watching as it provides a new way to look at ODEs and their behavior
nice spirit
nice teacher
LOL This being 2003... here I am watching in 2016.
Jesse Holton lucky you this math hasn't changed for centuries, only thing that changes is delivery!
Jesse Holton I'm watching it in 2018
Liz Perez Me too!
2018
Uploaded in 2008
Due to covid I'm taking ODE online, and my prof does not do lectures, just tells us to read the book and posts PowerPoints. Thank you Dr. Arthur Mattuck, you are a life saver, and thank you MIT Opencourseware for providing these videos for all of us struggling students.
It's been 25 years but this added up.
I am wondering that there was TH-cam 11 years back. # 2019#
It was so much better back then
(Pausing at 01:00) I don't get it. The course says "Differential Equations" and he starts by saying "I assume you all know what differential equations are". If that's what he assumes, what are the 33 lectures for?
stevenvh17 in the first course of calculus, you have to work with separable differential equations. He's just saying that you should have a general idea is to what differential equations are.
please do. Nobody asks for you to make this "stuff", nobody waits for you either. This teacher is great, nomatter the sign, he explains very well. I must say it's the first time I hear about it, after more than 5 years after high school, that's France.
I cannot thank MIT for doing this.
And I wish I had a porf Like Dr. Mattuck the first time I took differential equations a decade ago. I learnt (and assimiliated) more from this one video than I learned from that entire course possibly,a t least what I I retain from that class.
I wonder if these math people at MIT can work out how long it will take to pay off their student loans
Jimmy Harry at MIT they get sweet financial aid packages.
Jimmy Harry also they get 100k plus job out the door s0 not long.
Jimmy Harry probably not long. Nice joke.
MIT offers pretty good need based fin. aid
I think school is expensive while libraries are free,
For a vigorous purpose, you have to note that ONLY some continuous functions HAVE DERIVATIVES. But in most cases, yes, you have derivatives(especially for elementary functions).
bravo to the camera man/woman! very well done in capturing what the professor is focusing on!
cheers
13:58 he says it's year 2003. The video title says 2006. I feel betrayed :'(
I was going to make a comment about that, definitely seems odd to catalog it as Spring 2006 when the Professor says it is 2003.
Imagine walking into this as your first college class.... yikesss 😂
I was born approx 1 year after this lecture was recorded
i have tried to understand this from books but i cannot. but by watching this lecture it is very easy to understand. Arthur mattuck is a good teacher.
i wish my professors wrote big letters on the board.
All the people in this lecture are probably all working at NASA and places like that, smh.
@@chipcook5346 We are all thankful for your glorious input. It's people like you that make this a better place to live. 🌎
.
Son geniales amigos un abrazo desde San Jerónimo antioquia Colombia gracias
Great video! Thank you for uploading all these lectures, MIT!
Good Will Hunting brought me here. ..
I'm in precal and lookin into the future.
Good luck with pre calc
Passed it with a B
Elim Lacy you mean like college algebra trig sins cosines conics matrices composition functions etc? I'm doing it now scrunched into a 4 wk course we still have a while before we get to this bro u gotta do calc 1,2 and 3 first you did ur precal in one class though? My school divided it into college algebra and college trig.
John Cooley Well to think of it. Pre cal wasnt much of anything but a huge review of algebra and trigonometry. And there was some minor things extra like. Conioncs.... Im guessing conics is precalculus because conics is clearly the fundamental shapes that make up everything as we see it. That must be a huge headace cause that math is alota info. Good luck broski - john cooley
+Elim Lacy I don't know where you are now, but I'm a freshman in high school taking AP Calculus BC and I agree with this.
Thanks to the greatest professor and Open course ware for this wonderful lectures.
This is twenty years ago and still relevant and more! Sir is one of the greatest teachers I have come across .
why can't I find lectures 18,33,34 and 35 ?!! are they only for MIT students ?
abdalrahman mahdly : couldn't find most of them either, but managed to find the 33. Here it is man => ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-33-relation-between-non-linear-systems-and-first-order-odes/
Good luck with it. Cheers.
***** thanks :)
Abdulrahman Mahdaly Lectures 18, 34, and 35 are not available. Sometimes this is due to IP reasons, sometimes due to technical reasons (no audio or bad audio), and sometime because the lectures were not recorded. The reasons for missing 18, 34, and 35 are not given.
+MIT OpenCourseWare Could you tell us what topics were covered, please?
+effortless35 According to the course calendar: lecture 18 topic was "Engineering applications", lecture 34 topic was "Complex or repeated eigenvalues Eigenvalues vs coefficients", and the topics for lecture 35 were "Qualitative behavior of linear systems; phase plane". For more information see the course on MIT OpenCourseWare at: ocw.mit.edu/18-03S06
Anyone here in 2019?
Yaa bro..
Totally different from what I learnt, this is much deeper and wider
God almighty, he`s making it easy and accessible for everyone. this is something that no other American institution has done.
Ahh yes, my morning warm up
carajo algo estoy entendiendo
ODE's (ordinary differential equations) are not only useful, but often indispensable, in modeling a wide variety of physical problems. The essence of an DE is that it involves at least one derivative(i.e. one rate of change). If you are trying to develop a model that explains and predicts changes in population dynamics, for example, you must be able to account for growth rates (i.e. rates of change), and so you need DEs. In addition to physical problems, they are also important in economics.
Absolutely right. Mathematics is so aesthetically pleasing that way.
RECALCITRANT
This is all perfectly readable, you spoiled brats. I learned from it 10 years ago and it didn't even cross my mind to complain.
Man, you're cool.
Wow! Do you want a cookie?!
I have no idea what I'm watching, but I'm fascinated.
c++ ?
i + b = c
c + i = c1
c + b = c2
c + c1 = c3
c + c2 = c4
c4 + b = i++
int i = 54
int b= 2
int c = 666
shoot C++ is the best way for me to learn this kinda math, most people know this stuff they just can't put the symbols to common sense. C++ makes it easy in my opinion. I would say line element math would come in handy for designing turbo fins for rocket engines, heat emission, and wind tunnel testing.
He may be a professor but he hasn't a clue what apostrophes are for.
Lol I'm a history major why am I watching this?
Real question is: Why would anyone be a history major?
@@morganmitchell4017 Plan on going into education eventually
Fair enough. There are a few good reasons to do history, I was just thinking in most cases, history is something best studied in one's own private time. Especially in the UK, if you're a man studying history, don't expect to earn much, if anything, more than you would if you went straight into work.
Peter Jackson I’m only in my first year so I have plenty of time to change it too, but i’m just stuck because nothing else interests me and I don’t really have a passion for anything else. History excites me, so I figured why not teach if
Maxwell Passion and interest is something you can develop. It’d be nice to explore a bit whether its formal course work or clubs.
finally, I now can travel through time. Thx youtube AI, i promise you to see your older version in 1849 and i will make you smarter for my future search preferences.
I didn't expect the video to end so beautifully.
Thanks. I'm going to start differential Equations soon and a little birdie told me, these videos helped her SOOOOO much :D
@dearchiv "Cline" is a root word meaning slope as in incline, decline, or recline. To my knowledge, isoslope is not used as a synonym for isocline very widely, if at all, and all of the textbooks I've surveyed mention isoclines when referring to the method described in this lecture.
1.1 Million views , this generation isnt lost for sure
Awesome! I'm taking Elementary Ordinary and Partial Differential Equations in the Fall, I've been following the book the video lectures are going to be an amazing help! Thanks MIT for the free content.
In multivariate calculus it is the gradient of a vector field.
This concept can be utilized to evaluate surface integral problems too.
1+1=2 😎
Pretty good Professor. I learned more from this video than I have the past three weeks at my college, I'm having trouble understanding my professor. This really brings better insight unto what I have been reading in my text book.
Thanks MIT !
Thank you so much MIT. I know my class is going to be much easier now.
Wish I had this guy as a lecturer when I was at Uni