The Theory of Higher Order Differential Equations
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- เผยแพร่เมื่อ 21 ก.ค. 2024
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Previously in my ODE Playlist we've talked about the theory of 1st order or 2nd order differential equations. Now we turn to the more general nth order ODE, specifically focusing on linear homogeneous ODEs. A lot of the theory is the same, but we have a few complications to deal with. Firstly, we have a new Existence and Uniqueness theorem for linear ODEs. Next, we have the principle of superposition which allows us to take linear combinations of solutions and deduce new solutions. Finally we describe the method to find the general solution to an nth order ODE and use the Wronskian to verify linear independence of the fundamental set of solutions:
0:00 Linear nth order ODEs
1:52 Existence & Uniqueness
3:20 Superposition
5:00 General Solution
7:02 The Method
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The way you present complicated topics in such an elegant way is just brilliant! Why can’t you be my math professor QQ
Fantastic! Very clear and concise. Exactly what I was looking for. Thanks!
Professor, you have my upmost appreciation, thanks to you who manage to teach me what my college professor couldn't under 10 minutes.
Professor Bazett, thank you for an awesome analysis on The Theory of Higher Order Differential Equations. Many topics in Differential Equations are similar to each other.
I have a question can you define the algebraic structure behind this general nth order differential equation
Fancy all math videos from Dr. Trefor. If you search math tutorial video, this channel is a must -see.
Sir I have a doubt in propositional logic. If you can help me with a video then I would be grateful to you. The question is : how for all values of x implies there exist of x for particular P(x)?
Fantastic Lecture
just going to complete the playlist !
6 more
Thanks, I was totally lost with these topics till now :d. Do you think that we should be able to understand all this topics from a book quickly. Im asking because this same theorem is so hard to understand by reading it from a book. What is the difference, should we always watch videos to learn math?.
Really enjoyed the video
May I ask what is the wronskian? Is this like checking whether a matrix has Full Rank or not (rank deficient) in the Linear Algebra world?
Check out the previous video in the series where i introduce it. But yes, it has a tight connection to linear algebra as you suggest.
I am biased that I will grasp the topic that you explain where W[x] is not 0 (independent :)) of what the topic is.
Thanks a lot sir!!
Thanks a lot sir 🔥🔥🔥
What if ith derivative of y((0) is equal to zero but the others are not equal to zero? There is no such b for that case, so uniqueness fails?
Great content sir!
Glad you think so!
Thank you sir! You are perfect!
So nice of you!
Your videos should be getting way more likes but I mean WAY more likes.
Please Prof, Why while stating the general theorem, You defined F(x) = 0, Is it applicable only for the homogeneous ODEs ?
If you subtract the right hand side from both sides and include it in the F(x) you can make every equation equal to zero
@@DrTrefor does this mean ever equation can be a HDE?
When the solution of third order DE is y= c1 y1^2+c2 y2^2+c3?
Theory of higher order? More like "Terrific videos that are like no other!"
Good stuff!
Thanks!
Thank u so much sir
Thanks dr from Algeria
You're most welcome!
good
the number of bacteria on a plant follows a poisson distribution with parameter 60. find the probability of there being 55 to 75 bacteria on a plant
Gd afternoon professor. Plz let me explain that question. I got confused. (From Srilanka)
Do not trust, is April fools day.
someone in my undergrad once told me every function is analytic and I slept deeply that night
Your mic makes it annoying to hear you tho your explanation is incredibly good please s new mic
First!
nice!!
literally waxted my time and didnt understood a thing !!!!!!!!!
Then check out earlier videos. In context, all of this makes perfect sense. If the earlier videos dont make sense you need a primer on some prerequisites, like basic calculus