These lectures are of great quality and cost me nothing. Thanks to your efforts prof. You are helping many students who either can't afford quality maths education or sometimes have no access to quality education even if they pay.
I am suffering from the second. My professors aren't bad, but they don't want to put in the effort after looking how mediocre the rest of my class is, so I have to suffer because of it too
@@hannan044 No that isn't just the US it is part of every university course on differential equations. Stop beeing so condescending on the internet, it doesn't make you look smart
Dr. Trefor Bazett, thank you! After 9 years off maths and going back in to doing a Masters in Engineering this channel has been an absolute blessing. You deserve some serious recognition!
I spent over 10 hours trying to understand this from my school lectures and it only took 13 mins on here. Thanks a lot Trefor, at least I won't be clueless in my exam tomorrow
Literally Dr. Trefor, you are the best to help understand mathematics. The beauty of mathematics comes out in your videos!! I am going to make a daily schedule to listen to your videos. Thank you Sir.
I first watched this video when i was taking a linear algebra course in college. Now a year later i came back to this channel and these video's as a refresher and to prepare for my classes on dynamical systems. Great video!
Thank you for this series of videos. They help me a lot when trying to study ODEs on my own. Also, the visualizations are very good. I hope there'll be more videos concerning the applications of these equations in real physical cases, like those about mechanical vibrations. After all, thank you for all your works!
Thank you so much for the video! I watched it last year when I took intro to differential equations, and I'm watching it again this year as review for my engineering analysis class. Your explanations are perfect!
I would like to take this opportunity to say I love and appreciate all math teachers on UA-cam. Thank you all so much. Your existence brings me tears of joy after the tears of pain from not understanding anything that the textbook is trying to tell me. You are the light at the end of the tunnel, you are the angel that saves me in times of adversity. Thank you so much.
Thank you so much for your videos! They helped me greatly in passing Differential Equations and made a lot of things that were confusing in lectures really clear and concise! Couldn't have gotten the grade that I did without your extra help.
Hey Trefor! I have got a question that I can find no answer to and since you are a math Professor I hope you can help me. Its about partial differential equations (i know not exactly the topic of the video) in physics. My question is: How can we be sure that ,since we often can only find parts of the general solution of a pde, that this part represents the physical scenario? An example to clear things up: take for example the schrödinger equation. We usualy solve it by seperation of variables. However there are defenetly other solutions as well that are not seprable but still solve the equation, we just cant find them analitically. How can we then still make sure that the studied particle has the wave function (or one of the wave functions) that is/are given by the seprable solutions we found and not by another? Doesnt that basically destroy or chance of getting information abou the particle since the most general solutions to pdes are usualy such a wider class? Thanks in advance!
Definitely look up the various existence and uniqueness results for separable PDEs, this is what ultimately gives us a handle on the “halting problem” you describe.
thank u sir for soo much your efforts in explaining the topic in crystal and clear method, i know it is required soo much hardwork in editing and gathering the resources and deliver the best content thanksssss!!!!!
If i had watched your videos from the start i would be soaring in my DEQ class by now lol. Better late than never i guess as my next exam is in 2 days :,). Thank you so much for everything you are doing!!!!
Dang I didn’t realize this series is this recently made, do you have an idea when the series will end? These vids are so helpful to follow along while going through the book.
I wish I had you as a teacher. I'm taking this class online and the book doesn't have any examples at all, and the teacher is virtually nonexistent so I'm stuck scrambling for some sense of understanding and it's not coming at all.
Same here, my online class sucks, its like they take pride in complicating concepts that are actually simple once they are properly explained just to make you feel stupid. All the examples they give you are the ones that are so easy we could figure out ourselves, then the problems they throw at you to work on the exams are the ones that are the most twisted one offs that they never teach you how to solve that are the exceptions to all the rules you learn. I hate taking math online, its horrible. We cant even go over homework with the professor. I aced all my in person calculus classes, but online math is terrible
First off thank you so much for these videos they’re helping me tremendously. I had a question not super related to this video, but we’re learning variation of parameters right now. Do you have any materials that would help with that or a different way to do questions that ask you to solve using variation of parameters? I’ve looked at other videos and they make some sense but the explanation is too fast and steps are glossed over without explanations.
It is a really good video, the part which I love so much is the chart part. But I have a question, how to deal the particular solution equation like tcos(t)
Aha! I didn't realise that any 2 particular solutions would differ by at most some y_h, that makes so much sense. Finally I can do some well-justified guesswork.
Y 2prime - 2y prime - 3y =3e^2t = 2y-3y= 1 integral zero goes to infinity 3e^-2at = ye^-at e^at integral zero goes to infinity1/ a-t -= f(t) =v integral 2pie (z^2 + t^2) = 2 integral zt^2+ t^2/2 = z^3 + t^3/3 = 2pie t^2/3 =4/3 piet^3 absolute zero goes to infinite f(t) 1/a-s.
I'm still curious as to the ever convenient t^s that always saves the day whenever the inhomogeneous guess would solve the equation... since particular solutions are unique, up to adding some y_h, then surely this is a very nice coincidence, suggesting some far more direct approach to justifying why putting in enough ts will work out eventually?
Sir can you please explain why we can't simply find particular solution only . As the homogeneous solution eventually becoming zero . Sorry I don't know where I am lacking to grab the concept please help
Good question. There are some applications, where we are only interested in the long term solution, and finding the particular solution only, is good enough. An example, is steady state circuit analysis, where we don't care about the behavior during the first few milliseconds as the circuit reacts to the on-switch, we just care about the long term behavior. Electrical engineers have shortcuts for this, using complex numbers and the concept of impedance, that essentially solve differential equations with the Fourier transform (instead of the Laplace transform). While it is common to only care about the steady state solution, that doesn't mean that the initial transient isn't also of interest. There are applications such as vibration analysis and control systems engineering, where we are interested in how well-behaved a system response is, in its approach to the long-term behavior. For control systems engineering, ideally, we want a system to get to the desired steady state value as fast as possible, and minimize the overshoot. The initial transient behavior of a differential equation, as the homogeneous solution provides, tells us how the system responds to the input, and allows us to quantify how fast the controller responds. For instance, a critically-damped controller will bring the response to its steady state value as fast as possible without any overshoot, while an underdamped controller will get it there faster, but will overshoot and have the system output oscillate back and forth, as it settles to its steady state.
Thank you so much for the nice videos, it is really helpful. Right now I am having a problem with the following form: (dv/dt + L1*v = L2*(dx/dt+L3*x)), where t is the time variable, L1, L2, and L3 are constants, dv/dt, and dx/dt are the rate of change of v and x w.r.t time respectively. Is there a possibility to solve it without using Laplace? Is there a generic method to solve similar kinds of problems?
00:05 Introducing the method of undetermined coefficients 01:43 Combining homogeneous and particular solutions in non-homogeneous ODEs 03:16 Solving non-homogeneous ODEs using undetermined coefficients method 04:48 Solving non-homogeneous ODEs using undetermined coefficients 06:30 Choosing the particular solution using undetermined coefficients 08:03 Solving non-homogeneous ODEs using undetermined coefficients 09:38 Undetermined coefficients are used for non-homogeneous ODEs. 11:13 Using undetermined coefficients to solve non-homogeneous ODEs
This method doesn't work for all right hand sides, and the examples you give don't have an obvious "guess". Generally guess something of a similar form and hope to get lucky.
Hello Dr. Thanks for the lectures, they are really helping to me. I have the ff differential equations and need some ideas on how to start: solve a) x''=-4x^3+4x , b) y''=y^2-y?. Thanks.
These lectures are of great quality and cost me nothing. Thanks to your efforts prof. You are helping many students who either can't afford quality maths education or sometimes have no access to quality education even if they pay.
Glad they are hellping!
I am suffering from the second. My professors aren't bad, but they don't want to put in the effort after looking how mediocre the rest of my class is, so I have to suffer because of it too
I swear this channel explains stuff 10x better than my university's lecture videos actual livesafer
I bet you were sleeping during the lecture.
@@collegemathematics6698 noo way
this is a university topic?… is this the usa 🤣
@@hannan044 No that isn't just the US it is part of every university course on differential equations. Stop beeing so condescending on the internet, it doesn't make you look smart
That too in 10 mins 🗿
Dr. Trefor Bazett, thank you! After 9 years off maths and going back in to doing a Masters in Engineering this channel has been an absolute blessing. You deserve some serious recognition!
I love how even behind a screen you are aiming at teaching the topics by ensuring that your students grasp them, thanks sir
good catch
Haven't seen anyone delivering the concepts of ODE's better than this . Remarkable methodology.
Did differential equations 20 or 25 years ago. Make sense watching it 2x speed non-stop. Thank you.
I spent over 10 hours trying to understand this from my school lectures and it only took 13 mins on here. Thanks a lot Trefor, at least I won't be clueless in my exam tomorrow
Good job dr
You are one of the rare people on UA-cam who deserve like and subscribe
Man deserves a Nobel prize
This was a great refresher to ODEs. Thanks Dr. Trefor for the wonderful series.
Finally you received after your 7 years of hardwork congrats for 100k
Literally Dr. Trefor, you are the best to help understand mathematics. The beauty of mathematics comes out in your videos!! I am going to make a daily schedule to listen to your videos. Thank you Sir.
I first watched this video when i was taking a linear algebra course in college. Now a year later i came back to this channel and these video's as a refresher and to prepare for my classes on dynamical systems. Great video!
I never really understood why add Complementary Function and Particular Integral but now I do
Thanks for clearing a basic concept
The quality of education you are providing is just amazing :)
Very helpful , Thank You 🧡
Really refreshing to feel some enthusiasm while teaching and not just a monotone voice all along. Thanks !
I finally understand why any particular solution will work. Thanks! You always make material clear and engaging.
I taught I will just watch it and leave it but I found it a great video by great lecturer I need to download it fast.❤ U are too good sir
Thank you for this series of videos. They help me a lot when trying to study ODEs on my own. Also, the visualizations are very good. I hope there'll be more videos concerning the applications of these equations in real physical cases, like those about mechanical vibrations. After all, thank you for all your works!
You are most welcome!
The Gigachad submits to his teacher
There is Ate^-t I think 8:21, but it's not a problem. This video is amazing. Very well explained, love your content!
I was just noticing this and wondered if I made a mistake. thanks for pointing this out. I also believe is a minor error. Video is great.
It took me a 30 mins writing my problem again and again, thinking I made a mistake. Thank you for pointing out.
Congrats on 100k Dr. Bazett!
Thanks so much!!!
Thank you so much. I wish my proffesor explained with the joy you explain. I'll let you know if I pass my exam in 2 hours
Professor Trefor Bazett, thank you for an outstanding video/lecture on Undetermined Coefficients in Ordinary Differential Equations.
youre the goat bro my prof is a professional yapper and what you explained in 12 minutes takes him two 50 minute classes
Wow, this video cleared up what I didn't understand during my lecture, phenomenal teaching, thank you!
You are so so talented at lecturing. Thank you for putting these together!
Thank you so much for the video! I watched it last year when I took intro to differential equations, and I'm watching it again this year as review for my engineering analysis class. Your explanations are perfect!
You're very welcome!
This video about solving linear non homogeneous ODE's is the best on the internet in my opinion, thank you!
I have a midterm in two days, and your videos are saving my life!
Love this guy, I’ve been confused for a week but not anymore
So close to a 100K. Congratulations in advance!
Haha, thanks!!
He made it!
Was super confused on this after my lecture. This helped clear it up. Thanks king 👑!!
Just so helpful. Making my mathematical methods class a breeze!
Nice, you saved me in E&M and now again in another Physics class.
Dr. Trefor... The God head...
Thank you for sharing your knowledge, it does so much.
Such crisp presentation! Finally was able to complete my syllabus for ODEs and Lin Algebra
And, once again, Trefor managed to make sense of a week worth of lectures in under 13 minuits
I would like to take this opportunity to say I love and appreciate all math teachers on UA-cam. Thank you all so much.
Your existence brings me tears of joy after the tears of pain from not understanding anything that the textbook is trying to tell me. You are the light at the end of the tunnel, you are the angel that saves me in times of adversity. Thank you so much.
The variation of parameters is more convincing and more general method than undetermined coefficients.
Oh wow this video gave me a euraka moment, nowhere on the internet has actually explained WHY this works rather than how to use it
Ex. 2 highlights the fact that the pieces of the general solution must be linearly independent.
I have a quiz today on this topic, thanks for the brief but concise overview of it.
Thank you so much for your videos! They helped me greatly in passing Differential Equations and made a lot of things that were confusing in lectures really clear and concise! Couldn't have gotten the grade that I did without your extra help.
Hey Trefor! I have got a question that I can find no answer to and since you are a math Professor I hope you can help me.
Its about partial differential equations (i know not exactly the topic of the video) in physics. My question is: How can we be sure that ,since we often can only find parts of the general solution of a pde, that this part represents the physical scenario? An example to clear things up: take for example the schrödinger equation. We usualy solve it by seperation of variables. However there are defenetly other solutions as well that are not seprable but still solve the equation, we just cant find them analitically. How can we then still make sure that the studied particle has the wave function (or one of the wave functions) that is/are given by the seprable solutions we found and not by another? Doesnt that basically destroy or chance of getting information abou the particle since the most general solutions to pdes are usualy such a wider class? Thanks in advance!
Definitely look up the various existence and uniqueness results for separable PDEs, this is what ultimately gives us a handle on the “halting problem” you describe.
@@DrTrefor Thank you!
Thanks sir for your lectures it's really very helpful for me.
Best video I’ve seen on this
thank u sir for soo much your efforts in explaining the topic in crystal and clear method,
i know it is required soo much hardwork in editing and gathering the resources and deliver the best content thanksssss!!!!!
If i had watched your videos from the start i would be soaring in my DEQ class by now lol. Better late than never i guess as my next exam is in 2 days :,). Thank you so much for everything you are doing!!!!
For real the tutorial has a quite elaborate content. Thankyou
Dang I didn’t realize this series is this recently made, do you have an idea when the series will end? These vids are so helpful to follow along while going through the book.
this exact series is over, but I’m planning more related to ODEs for example Fourier series is next week
wow you just explained calculus in laymans terms...huge thanks.
Bro I wish you were my calculus professor here at BME! You make something so complex so easy to understand.
Thanks Dr. It was difficult before I storm this youtube video
open source textbook? mvp
How to find constants A, B, C, D, E? Can you please explain a bit? Thank you for teaching us.
plug them into the differential equation and then line up the resulting coefficients on each side
I have an ensuing test on this and variation of parameters and these videos are very helpful! Thank you!
very good explanation
Sir you definitely deserve more subscribe r.
Good job. I don't remember it being this easy but it looks easy now.
I wish I had you as a teacher. I'm taking this class online and the book doesn't have any examples at all, and the teacher is virtually nonexistent so I'm stuck scrambling for some sense of understanding and it's not coming at all.
Same here, my online class sucks, its like they take pride in complicating concepts that are actually simple once they are properly explained just to make you feel stupid. All the examples they give you are the ones that are so easy we could figure out ourselves, then the problems they throw at you to work on the exams are the ones that are the most twisted one offs that they never teach you how to solve that are the exceptions to all the rules you learn. I hate taking math online, its horrible. We cant even go over homework with the professor. I aced all my in person calculus classes, but online math is terrible
u the goat dog, i will dream about this lesson tonight and ace my midterm 💪
First off thank you so much for these videos they’re helping me tremendously.
I had a question not super related to this video, but we’re learning variation of parameters right now. Do you have any materials that would help with that or a different way to do questions that ask you to solve using variation of parameters? I’ve looked at other videos and they make some sense but the explanation is too fast and steps are glossed over without explanations.
I don’t have a video, but check the textbook linked in the description it covers them wrll
Thank you so much!
Congrats on 100k Subs!
Thank you so much 😀
you are a lifesaver, ty Dr. Trefor~
Sir, You are awesome.
Thank you Prof, you are an awesome teacher
Thank you! 😃
Was so amazing I didnt even blink. Perfect
excelent! you have no idea of how much this helps, thx.
Glad it helped!
man you are a gold mine
Hi, thank you for the videos, helped me a lot. In the guesses (9:17), the multiplicity shouldn't apply?
thank you so much for this lecture , it is helping me more for my preparation ,thanks again
I just wanna say, u are amazing. !!!
Thank you so much Dr. Trefor!
It is a really good video, the part which I love so much is the chart part. But I have a question, how to deal the particular solution equation like tcos(t)
Aha! I didn't realise that any 2 particular solutions would differ by at most some y_h, that makes so much sense. Finally I can do some well-justified guesswork.
you deserve more subscribers
Y 2prime - 2y prime - 3y =3e^2t = 2y-3y= 1 integral zero goes to infinity 3e^-2at = ye^-at e^at integral zero goes to infinity1/ a-t -= f(t) =v integral 2pie (z^2 + t^2) = 2 integral zt^2+ t^2/2 = z^3 + t^3/3 = 2pie t^2/3 =4/3 piet^3 absolute zero goes to infinite f(t) 1/a-s.
incredible lesson
i was so bad at maths until i came across this channel
Thank you Dr. Trefor
❤ from india 🇮🇳🇮🇳🇮🇳🇮🇳
Your videos are wonderful, can't thank you enough
you're a live saver man
This is brilliant. Thank you so much!!!
you sir are a LEGEND
I'm still curious as to the ever convenient t^s that always saves the day whenever the inhomogeneous guess would solve the equation...
since particular solutions are unique, up to adding some y_h, then surely this is a very nice coincidence, suggesting some far more direct approach to justifying why putting in enough ts will work out eventually?
Sir can you please explain why we can't simply find particular solution only . As the homogeneous solution eventually becoming zero . Sorry I don't know where I am lacking to grab the concept please help
Good question. There are some applications, where we are only interested in the long term solution, and finding the particular solution only, is good enough. An example, is steady state circuit analysis, where we don't care about the behavior during the first few milliseconds as the circuit reacts to the on-switch, we just care about the long term behavior. Electrical engineers have shortcuts for this, using complex numbers and the concept of impedance, that essentially solve differential equations with the Fourier transform (instead of the Laplace transform).
While it is common to only care about the steady state solution, that doesn't mean that the initial transient isn't also of interest. There are applications such as vibration analysis and control systems engineering, where we are interested in how well-behaved a system response is, in its approach to the long-term behavior. For control systems engineering, ideally, we want a system to get to the desired steady state value as fast as possible, and minimize the overshoot. The initial transient behavior of a differential equation, as the homogeneous solution provides, tells us how the system responds to the input, and allows us to quantify how fast the controller responds. For instance, a critically-damped controller will bring the response to its steady state value as fast as possible without any overshoot, while an underdamped controller will get it there faster, but will overshoot and have the system output oscillate back and forth, as it settles to its steady state.
@@carultch so in short to get the information about initial conditions. Thank you for clarifying this
Thank you so much for the nice videos, it is really helpful.
Right now I am having a problem with the following form: (dv/dt + L1*v = L2*(dx/dt+L3*x)), where t is the time variable, L1, L2, and L3 are constants, dv/dt, and dx/dt are the rate of change of v and x w.r.t time respectively.
Is there a possibility to solve it without using Laplace?
Is there a generic method to solve similar kinds of problems?
00:05 Introducing the method of undetermined coefficients
01:43 Combining homogeneous and particular solutions in non-homogeneous ODEs
03:16 Solving non-homogeneous ODEs using undetermined coefficients method
04:48 Solving non-homogeneous ODEs using undetermined coefficients
06:30 Choosing the particular solution using undetermined coefficients
08:03 Solving non-homogeneous ODEs using undetermined coefficients
09:38 Undetermined coefficients are used for non-homogeneous ODEs.
11:13 Using undetermined coefficients to solve non-homogeneous ODEs
Thank you so much sir
12:05 What if the right hand side is like , say... sin(t^2 + 1) , or e^(sin t) ?
This method doesn't work for all right hand sides, and the examples you give don't have an obvious "guess". Generally guess something of a similar form and hope to get lucky.
@@DrTrefor Thank you , sir..... we don't have an obvious guess for such examples , that's why I asked if there is a way to solve such examples
You are a legend my friend
he is physical manifestation of not every hearo wear cape.
I wear a cape on Halloween;)
This guy is wayyyyy to excited and hyped up to teach haha
Hello Dr. Thanks for the lectures, they are really helping to me. I have the ff differential equations and need some ideas on how to start: solve a) x''=-4x^3+4x , b) y''=y^2-y?. Thanks.
The annihilator approach is more systematic for example y''+25y=sin(5x)
Assuming a solution in the for of Asin(5x) won't work
so what do we do?
@@aashsyed1277 use annihilator
@@killua9369 ok
@1:18 by this logic, wouldn’t y_p + an infinite sum of y_h also be a solution? Since y_h will all end up being 0
you>>my teacher
Thank you! that was very well explained.
Thank you very much sir 🔥🔥🔥