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
@@hann8528 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
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!
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.
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!
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.
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 would like to take this opportunity to say I love and appreciate all math teachers on TH-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.
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!!!!!
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.
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!!!!
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)
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
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?
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?
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.
thank you for your work, it is amazing and easy to get it. But I have got a question about your second exercise. On solving Homogeneous way, you put -3y = -3(Ate^-t). is this alright? But, I looked at my teacher solution and he actually put, -3y = -3(Ae^-t). Hope you have got my point and looking forward for yr replay. thanks
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.
Do you have any plans on doing a course in Foundations of Mathematics, I have the by Stewart, but I'm afraid that I can't do it by myself. 😟 you did a great job with calculus.
@@DrTrefor yeah, but I liked to do a foundations before leaping into graph and enumeration... But thanks anyway ♥️ I'd be lost without great teachers like you.
You're probably thinking of the method of variation of parameters, where we use two integrals to find the particular solution. That's a method that works with the kinds of functions that aren't simple exponentials, simple trig, and polynomials, that play nicely with diffEQ's. For the method of undetermined coefs, you don't need to do an integral to find your yp. You just construct an arbitrary combination of functions of the same form, as your given RHS, with arbitrary coefficients, and then apply to the original diffEq to solve for those coefficients.
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 love how even behind a screen you are aiming at teaching the topics by ensuring that your students grasp them, thanks sir
good catch
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 🤣
@@hann8528 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!
Haven't seen anyone delivering the concepts of ODE's better than this . Remarkable methodology.
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
This was a great refresher to ODEs. Thanks Dr. Trefor for the wonderful series.
Did differential equations 20 or 25 years ago. Make sense watching it 2x speed non-stop. Thank you.
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!
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 never really understood why add Complementary Function and Particular Integral but now I do
Thanks for clearing a basic concept
Finally you received after your 7 years of hardwork congrats for 100k
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
The quality of education you are providing is just amazing :)
Very helpful , Thank You 🧡
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!
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
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.
I finally understand why any particular solution will work. Thanks! You always make material clear and engaging.
Really refreshing to feel some enthusiasm while teaching and not just a monotone voice all along. Thanks !
You are so so talented at lecturing. Thank you for putting these together!
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
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.
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!
So close to a 100K. Congratulations in advance!
Haha, thanks!!
He made it!
Just so helpful. Making my mathematical methods class a breeze!
And, once again, Trefor managed to make sense of a week worth of lectures in under 13 minuits
Was super confused on this after my lecture. This helped clear it up. Thanks king 👑!!
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
I have a quiz today on this topic, thanks for the brief but concise overview of it.
Man deserves a Nobel prize
Love this guy, I’ve been confused for a week but not anymore
I have a midterm in two days, and your videos are saving my life!
I would like to take this opportunity to say I love and appreciate all math teachers on TH-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.
This video about solving linear non homogeneous ODE's is the best on the internet in my opinion, thank you!
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!
The variation of parameters is more convincing and more general method than undetermined coefficients.
Hi, thank you for the videos, helped me a lot. In the guesses (9:17), the multiplicity shouldn't apply?
Nice, you saved me in E&M and now again in another Physics class.
youre the goat bro my prof is a professional yapper and what you explained in 12 minutes takes him two 50 minute classes
Such crisp presentation! Finally was able to complete my syllabus for ODEs and Lin Algebra
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!!!!!
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.
Bro I wish you were my calculus professor here at BME! You make something so complex so easy to understand.
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!!!!
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
Thanks sir for your lectures it's really very helpful for me.
I have an ensuing test on this and variation of parameters and these videos are very helpful! Thank you!
Good job. I don't remember it being this easy but it looks easy now.
Congrats on 100k Subs!
Thank you so much 😀
Best video I’ve seen on this
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)
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
very good explanation
Ex. 2 highlights the fact that the pieces of the general solution must be linearly independent.
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?
For real the tutorial has a quite elaborate content. Thankyou
open source textbook? mvp
Thanks Dr. It was difficult before I storm this youtube video
Was so amazing I didnt even blink. Perfect
wow you just explained calculus in laymans terms...huge thanks.
Dr. Trefor... The God head...
Thank you for sharing your knowledge, it does so much.
excelent! you have no idea of how much this helps, thx.
Glad it helped!
u the goat dog, i will dream about this lesson tonight and ace my midterm 💪
incredible lesson
Sir you definitely deserve more subscribe r.
man you are a gold mine
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?
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.
Thank you Prof, you are an awesome teacher
Thank you! 😃
thank you so much for this lecture , it is helping me more for my preparation ,thanks again
thank you for your work, it is amazing and easy to get it. But I have got a question about your second exercise. On solving Homogeneous way, you put -3y = -3(Ate^-t). is this alright? But, I looked at my teacher solution and he actually put, -3y = -3(Ae^-t). Hope you have got my point and looking forward for yr replay. 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
you're a live saver man
at 8:35 you had an exponent with positive t in the y double prime
you are a lifesaver, ty Dr. Trefor~
I just wanna say, u are amazing. !!!
Thank you Dr. Trefor
Thank you so much sir
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.
Thank you so much Dr. Trefor!
i was so bad at maths until i came across this channel
This is brilliant. Thank you so much!!!
Your videos are wonderful, can't thank you enough
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.
really great video, thanks
you sir are a LEGEND
Perfect as usual.
thank you!
you deserve more subscribers
Hello teacher, Do I have the permition to take a small note from your videos?
Do you have any plans on doing a course in Foundations of Mathematics, I have the by Stewart, but I'm afraid that I can't do it by myself. 😟 you did a great job with calculus.
I do have a bunch of overlap with this in my "discrete math" course but not a dedicated course thus far
@@DrTrefor yeah, but I liked to do a foundations before leaping into graph and enumeration... But thanks anyway ♥️ I'd be lost without great teachers like you.
This guy is wayyyyy to excited and hyped up to teach haha
You are a legend my friend
You are a legend thanks
Thank you! that was very well explained.
OMG I needed this video! 🥳🥳
Glad it helped!
@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
Thank you very much sir 🔥🔥🔥
Is particular integral same as the particular solution Yp? I have seen people use the term "particular integral" in non homogeneous cases?
You're probably thinking of the method of variation of parameters, where we use two integrals to find the particular solution. That's a method that works with the kinds of functions that aren't simple exponentials, simple trig, and polynomials, that play nicely with diffEQ's.
For the method of undetermined coefs, you don't need to do an integral to find your yp. You just construct an arbitrary combination of functions of the same form, as your given RHS, with arbitrary coefficients, and then apply to the original diffEq to solve for those coefficients.