How to Solve a Second Order Linear Homogeneous Recurrence Relation(Distinct Real Roots Case)
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- Опубліковано 28 січ 2020
- In this video I will show you how to solve a second order linear homogeneous recurrence relation. The problem in this video is the case with distinct real roots.
Good thing I paid my university tens of thousands of dollars so a guy on UA-cam can explain this random set of numbers that doesn't mean anything
Finally found a short simple and easy way to understand this, thank you.
Me too👍👏
I don't usually comment, but this video was so clear and concise and desperately needed while studying for a final. Great work!
Love it. Straight to the point. I was tackling my textbook for ages trying to figure it out. Glad I didn’t give up and looked here!
Fantastic video my friend. Your love and enthusiasm for math and teaching are very apparent and much appreciated.
I saw over 5 videos everything they did was complicated, but this man right here! He is the best in the bussiness💯
Thank you so much, I've spent all day trying to figure this out without success and your video managed to teach me in under 6 minutes. Thank you so much
Excellent!
Thanks man, you are an absolute LIVE AND ACADEMIC CAREER SAVER!
A very nice and simple explanation of a topic that is often buried in highly obtuse treatments. Was recently watching a video on the balancing numbers by Michael Penn who is fantastic but Lord have mercy what a complicated route he took to find a closed formula for a similar sequence with signature 6 - 1 and starting terms of 1 and 6. The oeis contains thousands of these sequences which are all indexed
Living Legend didnt understand a thing from my professor. This is super helpful and it only took me 6 minutes to understand. THANK YOU!!!!!!
You are the best
This is absolutely amazing. I've been trying to understand this topic and been looking all over that internet and all of the recorded lectures of last years and I was just really struggling because my exam was in 2 days. This helped!!!
Glad it was helpful!
THIS IS SO LOUD AND CLEAR✅✅
you're a life saver, thanks so much
This is soo satisfying! Awesome video!
omg you saved my life! thanks a lot for the simple and clear explanation
Bet explanation EVER!! Thank you sooo much
This make so much sense and meaning and can relate to it a lot and understand a lot from it. Thank you.
Wow, Awesome, I like your way of teaching, Thanks
This video was really helpful understanding this topic. I’m burning through my discreet mathematics book doing self and study and sometimes. I wonder when and why a topic like this is important to know. In essence I wish to know some of it applications to real problems. Cheers.
So simple, really understood. Thanks man
You are welcome!
Can't believe it my teacher write answers in two page 😂 and you solve this in one page hats off sir ❤
Thank you, this helped me a lot.
Thank you so much!!! From the pattern that you have written, when a_n = x^2 and a_(n-1) = x and a_(n-2) becomes the constant, it means that a_(n+1) = x^3 and a_(n+2) = x^4 and so on! That solved the problem I am working on right now. Really really thank you!! I wish I could meet you in person and give you a big hug!
so clear, ty dude!
I was hoping you'd derive it : ) thanks for the content.
ahh yeah I should that!!!
fire. thank you very much!!
The best and the most clear one also short video 🙏
Thank You, the video helped a lof to understand
Wow I looked this up because struggling with homework and get a video from one of my favourite channels and coincidentally doing the first question on my homework haha thank you
🥰🥰you are the best of best keep going.
Good job, I am fascinated
Great video, thank you
great vid thanks for your lecture
Ahaha I saw your "math professors be like" video a while back, nice to actually be learning something from you now :)
haha cool
I was stuck after getting a single root in my problem you really helped
One video , one problem and a half of theme👍
thank you so much, only one Q ((when you find c2 why did you substitute in the first condone eq))?
Thank you soo much its 3am.I have my discrete math exam at 10am and i totally forgot how to do this for some reason.thank you man
Hi. Could we solve such a relation using backtracking?
How does the solution change if add 1 to all the subscripts (ie. a_n would become a_(n+1), etc.)?
so helpful, my professor zooms through class. you are math jesus i swear.
Hi, great video! I was wondering why you can say that a_n = x^2?
thankkk u sm u save me :)
Great explanation
Thank you!
This helped me understand this concept a lot more in time for my finals. Thank you so much!
Shukran a sahbi
Is this based upon generating functions?
THANK YOU
Wow! Thanks.
thank you, very helpful
You're welcome!
Thank you sir
For repeated root. Does it matter if so: C1x2n + C2xnx2n or so: C1xnx2n + C2x2n?
Thank you
great explanation
i dont understand though whats the logic behind the n exponent in:
an=c1x2^n+c2x3^n
like why is it suddenly an equal exponent for both parts, when before in the characteristic equation we had different exponents, and even in the first one, when going from a_n=5a_n-1-6a_n-2, to the characteristic equation, first we get that: a^n=5a^n-1-6a^n-2
again, thanks
I'm wondering from where did you get the "-2" number at 4:46 in the video?
I was following up until that point.
He told he will multiply (1=C1 + C2) by -1, and got -2 = -2C1 -2C2. Listen carefully
You can add, multiply, divide and subtract anything you want as long as you do it to both sides. He's trying to find the values for C1 and C2. He multiplied both sides by -2.
Amazing
What happens when only 1number a0 is given? e.g. order1 stuff? Thanks again
Hmmm I'd like to know why it has that form though. Any explanation about that?
its nice to have such clarity but i still cannot understand why change a(n) to x^n and then get the final expression as you have written but why x^n /x^2 (in your case) what does it really mean
to change a(n) to x^n and why are we doing it
Thank you sir Isaac Newton!
You are very welcome!
Thank you so much, tommorow i have class test
Good luck ❤️
Holy shit your channel name is spot on
Been freaking out all day on watched numerous videos read my text was stumped
watched this and actually have a clue wat to do now
what if it is just a_n = 6a_(n-2)
why we replace an by x² in the first step ?
BLESSS UPPPPPPP
can you explain how to solve this: An=5^(n-1)+2An-1 A0=1? thanks
What if it has no real roots?
What happens when I can't use systems of linear equations..?
2:39 what does 'recap' mean? I'm not good at english
it just means "let's go over it again":)
Thank you
I'm watching your video with respect in Korea
@@user-yc3ls4nq7o oh wow awesome!!!
what is the equation when x=alpha +- beta * i
I didn't know how you got C2 and I'll dream about it all my life
I knew i could trust you
Make some videos when the characterstics root is complex
oh yes, good idea, thank you so much, I will:)
Why it works? Can someone send me to a reference?
I would like to understand more about why this works and no how to apply it
Hey Hallie!
Hey Hallie!
why am I paying 3 Grand for a shitty teacher in university when this guy is much simpler and smoother!
What happens when ace of 0 = 0
with the multiplication by -2
I know I am years late whatever. Is it x^2 because it is a second degree because we have an n-2 term. Thus if there was an n-5 it would be degree 5 and I would instead say a_n=x^5. I think I get it but clarity is always nice. Thank you all either way!
I get it now, I answered my own question. TY!
yo but why can we just say that in the first place? that x^2 IS a_n and so on
Very easy until your professor asks you to prove with strong induction!
nobody noticed that he looks like jeff bezos ?
Thank you so much sir
Love from India
You are welcome!
wow, this absoluting the best video i've watched. do you have paypal or something. I want to show my appreciate to you.