NON-HOMOGENEOUS RECURRENCE RELATIONS - Discrete Mathematics
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- เผยแพร่เมื่อ 6 พ.ค. 2015
- Learn how to solve non-homogeneous recurrence relations. In this video we solve nonhomogeneous recurrence relations. This requires a good understanding of the previous video.
#DiscreteMathematics #DiscreteMath #RecurrenceRelations
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![[Discrete Mathematics] Nonhomogeneous Recurrence Relation Examples](http://i.ytimg.com/vi/UVuSLfdcT_Y/mqdefault.jpg)
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I'was reading the two pages of my book for over 2 hours trying to figure out what is going on and y just explained everything in the first 8 minutes. Thank you.
thanks so much man. These vids saved my ass last term when i took discrete 1 and they're doing it again this term with discrete 2. Your explanations and examples have been much easier to grasp than any lectures ive gotten from either of my professors. These two classes have been my hardest in college so far and i just wanna say thank you for making it easier for myself and a lot of other people!
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same for me even after 4 years
@@baroksander152 how'd it go?
Thanks again for this series, Mr. Trevtutor. Hugely helpful.
Your videos are insanely helpful.... I was stressing out about my final exam, but I feel much more confident. Thank You!
Thanks a lot for the great explanation!
Hey Trev! Thanks so much for the videos. Saving my life from impeding doom! Just curious, do you happen to have a video on non-homogeneous Recurrence relations with constants instead of like a^n? ex: An - 4an-1 + 4an-2 = 20
Trev, I can't thank you enough for your help.
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Awesome videos with great Explanation!!!
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crystal clear. Thank you respected sir.
Thanks a lot for the great explanations. It was helpful.
I had really weird fractions but I still got a working solution, thanks a lot!
Thanks sir, you helped me a lot!
Got benefitted, thanks a lot.
Can Someone Please help me with this one :
A(n) = 7A(n-1) - 10A(n-2) + n
and this one
A(n) = 2A(n-1) + 1
Infact +TheTrevTutor can you please make videos on the cases you left out (constant,n,n^2)
Thank you so much! Your video saved my life!!!!!
It is really similar approach like how we solve for 2nd order differential equations, we have to use the auxiliary equation to find roots as for the complementary function which in for recurrence relation we call it as characteristics equation and also solve the same way to find particular function which is quoted same in this recurrence solution solving methods
Best explaination of non homogenous reuccurence relations....keep it up
10/10 man. Pretty helpful
Awesome video/explanation! I just have one question. In the "Before we begin, Given:" part, in the top equation, it seems the subscripts of each pair should add up to n+1, so shouldn't the last term be alpha_(n+1-k)*a_k? Or are we assuming that n=2k? Thanks!
19:12 are there not restrictions though? if the sequence is 12030, there's a 3 to the right of a 0, so it can't be counted? or am I misunderstanding something?
my textbook made this chapter look menacing but our King Trev has come clutch once again
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You're a lifesaver man
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This is really helpful
great job. please i need examples on the other guessed soluitons. like n, n^2,...
The solution of the first one at 09:28 is interestingly enough, the derivative of a_n. Mere coincidence...but still cool!
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how do you solve : an-4an-1=n^2 in particular form ?
and what if f(n)=n-1, do we treat n as f(n) and 1 as number. my recurrence relation is a(n) =a(n-1) + (n-1)
In the second example why didn't you multiply the particular solution's terms with n+2, n+1 and n respectively as you did in the first example??
what if at the same time we have 2^n + n + 4 (at the right of the =) ?
Could you upload the steps we should follow written at the top?
you make youtube a better place.
Hi Trev. Thanks for your videos.
How would you solve the same equation as in this video if the equation equalled 1/3^n?
I do like your video!
thank you
Awesome video
Should we multiply it by n even if the homogeneous solution is in terms of 2 ^n+1
Why do we multiply 2^n by n for the inhomogenous solution? I am not quite understanding the problem with the similar roots? ...
What about a linear recurrence involves a no homogenous part of with n*a^n ?
i.e. g(n) = 6g(n-1) - 9g(n-2) +n * 3^n
Can we still guess the particular solution as n^m*A*a^n ?
the knowledge is good but the voice is TOO soothing, it is not good when you pull an all-nighter last minute before the exam haha
Absolute legend
Very nice
Thanks
if i switch a(n)-a(n-1) to a(n+1)-a(n), does the formula still work？
Thanks for the amazing videos. What should be the guess for particular solution when F(n) is a polynomial?
I am trying to solve An+3 - 3An+2 + 3An+1 - An = 3 + 5n
ax^3+bx^2+cx+d would be your guess.
@@Trevtutor why is that?
Skip my Discrete Math textbook. I'm just watching TheTrevTutor.
The only part that I am stuck at is why the eq. an = an(h)+ an(p) holds. Vectorial explanation, unfortunately, could not make it clear. Other than that, it was great
Thanks this helped me a lot for my exams
What is the an(p) of the f(n) 3^n+1
This video is useful even after 6 years
Sorry I have a question in which case. We use a matrix method or how will I know if am I needed of using matrix method
How to find the domain of n in this type of questions??
why is the solution(procedure) to a sequence sooo similar to the solution of a differential equations, be it homogenous or non homogenous
assume An is a function of differentiation and the solution becomes same
how can i pay you?
what will be the guess if after the right side of the equation is n*(4^n) ???
At 1:26 Shouldn't it be C(k+1) * a(n-k+1) instead of a(k)?
How do you procced if alfa or beta is zero? I for example have a0=0 -> alfa+beta = -(1/8), and a1=1 -> alfa-6beta = (3/4).
With the help of a matrix I get alfa = 0 and beta = -(1/8). My roots are 1 & -6, and my guess is A2^n
How to solve an=an-1=2^n ,Silimlar to given example but im stuck
what a good video ... I looked up discrete math with recurrence and a bunch of Indian people came up, had no idea what the hell they are talking about. Thanks for the clear and detailed videos.
When doing the particular solution part of the 2nd example problem, why didn't you multiply the terms with n?
16:18 alpha should equal to -4/5
oh he fixes it hahaha
How to guess when g(n) is some scary stuff like 2^n + n ^2 + n +c .....?..I encounter such maths at Rosen's book and inable to solve...please help..
I didn't get the a0 and a1 part. Can anyone help me out?
How to solve An-4An-1+4An-2=(n-1)2^n
At 23:17 i was thinking that a0 should be 0 as there is no string of lenght zero (it just doesn't make sense). Please help
I guess that is because there is just one string of length zero. The NULL string. Taking this one from the Automata Theory not sure if it applies here
Super late reply, but yeah. There is exactly one way to make an empty string. That's also why zero factorial is equal to 1: 0! = 1
Hello , Can anyone solve my doubt?
At 6:20 the term a(n+1) is being multiplied by A*2^(n+1) * (n+1)............i.e, mutiplied by n+1 but at 13:10 why (n+2) is not multiplied ?
It's because at 6:20 the roots are similar i.e 2^n whereas at 13:10 the roots are not similar , and if you still don't get it then go through the homogeneous recurrence relations part.
I didnt understand 5,05
Because; first you said that An+1 - 2An = 3n (0.35) but you continued as An+1 - 2An = 2n (5.05)
Can you help me,please ?
which software are you using to freely write this ?
+Brain Freeze Windows Journal
How do you get 17 in 17/20?
This method does not work with constants since you always end up with 0 when doing the particular solution
3:26
for f(n) = r^n
a(n)(p) should be A*(r^n)*n
it depends kiddo.
@4:35 isn't the equation supposed to be 1-2r=0
Trev can you please eighteen me on how to find initial condition
-2^n = -1, -1^n=-1 [ 15:40] , Everything else looks good and is well explained thank you
i am having problem finding the particular solution of the last Q
If someone is stupid and/or tired like me and wondering what happened to beta at 4:23 it's not there cause the characteristic function is linear.. 1 root..
Your videos are nice, but pleae be careful while using alphabets for constants, this r at 2:56 got me confused and got me turn back to homogeneous video.
Or, you could just use the z-transform and inverse-z transform.
I didn't get why did we multiply with n
negative number the power of zero is negative one why you say 1 in the second question?
In the last question suppose if the number is 1110322.here is also a 3 right of 0.This kind of cases are not covered by your Example.Elucidate me If I m wrong.
+Mayank Singh This sequence doesn't satisfy the formula in the video, because the formula was made like this: Let a(n) mean the amount of n-digit sequences that don't have a 3 anywhere to the right of a 0. If we have such an n-digit sequence, and its last digit is 0, 1, or 2, then the rest isn't just any sequence, it forms an (n-1)-digit sequence with no 3 to the right of a 0. And how many of those are there? a(n-1).
16:10 how is 16/20 equal to alpha, and then alpha is equal to 16/20? Shouldn't it be -16/20?
Can anyone help with the particular solution (guess) for : n + 2^n ?
(edit) Never mind, i got it: a_n = 2^n + a_n+2 - a_n+1,
(edit) Wait...maybe it's not.
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No Homo.
love u too
Alpha should equal to -4/5
Can anyone help me in this question a_n - 6*a_n-1 + 8*a_n-2 = n*4^n, with a_0 = 8, a_1 = 22, Please someone help me
At 21:26 how a0=1 ?
there is only one way to get a string of length 0
ok