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!
the way my lecturer DID NOT share YOUR video as the replacement for her lectures is just ugh saddening. Thank you very much for making me understand this topic.
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
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?
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
Loved the video and it was super helpful. Have a quick question tho, for 21:29, how do you know that there are only 1-string of zeros?? I am having a little trouble understanding the logic. And also how do you know to set the n >= 1for the final word problem?
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)
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.
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 ?
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.
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
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.
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
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!
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..
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
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).
![[Discrete Mathematics] Nonhomogeneous Recurrence Relation Examples](http://i.ytimg.com/vi/UVuSLfdcT_Y/mqdefault.jpg)
![[Discrete Mathematics] Nonhomogeneous Recurrence Relation Examples](/img/tr.png)
![[ MATH OLYMPIAD - SUMMATION ] HOW TO SOLVE THIS GEOMETRIC SERIES with RATIO TEST](http://i.ytimg.com/vi/YXsyRhAIgi4/mqdefault.jpg)
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!
wow! i have been trying to crack this all day and failed and this vid told me evth i needed to know in 23 mins! amazing man, keep it up
my prof is nothing compared to you. If i pass my midterm tomorrow it'll be because you saved me
So, how'd you go!
Was quite a while ago but I think u pulled in a B+ overall? Not too bad actually but could have been better for sure 😀
It's d day for me today
same for me even after 4 years
@@baroksander152 how'd it go?
the way my lecturer DID NOT share YOUR video as the replacement for her lectures is just ugh saddening. Thank you very much for making me understand this topic.
you make youtube a better place.
Thanks a lot for the great explanation!
This guy saving our semesters !!!!!!!!!!!!!!!!!!!!!!!!!!
you are helping me greater than any teacher
I love you, my friend and I are watching your video and you just saved our lives.
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
Your videos are insanely helpful.... I was stressing out about my final exam, but I feel much more confident. Thank You!
-2^n = -1, -1^n=-1 [ 15:40] , Everything else looks good and is well explained thank you
Perfect . . . just Perfect . . . Your page helps me to pass courses
my textbook made this chapter look menacing but our King Trev has come clutch once again
Trev, I can't thank you enough for your help.
The solution of the first one at 09:28 is interestingly enough, the derivative of a_n. Mere coincidence...but still cool!
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?
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
Thanks again for this series, Mr. Trevtutor. Hugely helpful.
Could you upload the steps we should follow written at the top?
Thank you so much! Your video saved my life!!!!!
You're a lifesaver man
Loved the video and it was super helpful.
Have a quick question tho, for 21:29, how do you know that there are only 1-string of zeros?? I am having a little trouble understanding the logic.
And also how do you know to set the n >= 1for the final word problem?
Best explaination of non homogenous reuccurence relations....keep it up
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 had really weird fractions but I still got a working solution, thanks a lot!
16:18 alpha should equal to -4/5
oh he fixes it hahaha
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)
This video is useful even after 6 years
Thanks a lot for the great explanations. It was helpful.
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.
Got benefitted, thanks a lot.
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 ?
Skip my Discrete Math textbook. I'm just watching TheTrevTutor.
Thank you... It was really helpful Vedio...
Ur videos are amazing.A life saver for sure :)
thank you very much!!! You are an amazing teacher!!!
10/10 man. Pretty helpful
thank you
Awesome videos with great Explanation!!!
crystal clear. Thank you respected sir.
teach me all subjects pls mannnn!!! you teach too good! Thank you....I hope of getting good marks because of you.....
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.
At 1:26 Shouldn't it be C(k+1) * a(n-k+1) instead of a(k)?
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
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
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?
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.
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
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
3:26
for f(n) = r^n
a(n)(p) should be A*(r^n)*n
it depends kiddo.
Thanks this helped me a lot for my exams
Thanq very much sir u are saving me
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??
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)
When doing the particular solution part of the 2nd example problem, why didn't you multiply the terms with n?
This is really 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!
Absolute legend
what if at the same time we have 2^n + n + 4 (at the right of the =) ?
Thanks sir, you helped me a lot!
Should we multiply it by n even if the homogeneous solution is in terms of 2 ^n+1
Amazing just Amazing thank u very much
so helpful thanks
Awesome video
@4:35 isn't the equation supposed to be 1-2r=0
Why do we multiply 2^n by n for the inhomogenous solution? I am not quite understanding the problem with the similar roots? ...
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..
what will be the guess if after the right side of the equation is n*(4^n) ???
How do you get 17 in 17/20?
great job. please i need examples on the other guessed soluitons. like n, n^2,...
I do like your video!
What is the an(p) of the f(n) 3^n+1
Thanks a lot Sir.
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
Very nice
16:10 how is 16/20 equal to alpha, and then alpha is equal to 16/20? Shouldn't it be -16/20?
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
if i switch a(n)-a(n-1) to a(n+1)-a(n), does the formula still work？
Thanks
how do you solve : an-4an-1=n^2 in particular form ?
how can i pay you?
Can anyone explain to me how we are identifying the homogeneous part from the entire equation?
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..
How to find the domain of n in this type of questions??
How to solve An-4An-1+4An-2=(n-1)2^n
Trev can you please eighteen me on how to find initial condition
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 ?
I didn't get the a0 and a1 part. Can anyone help me out?
This method does not work with constants since you always end up with 0 when doing the particular solution
which software are you using to freely write this ?
+Brain Freeze Windows Journal
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).
How to solve an=an-1=2^n ,Silimlar to given example but im stuck
At 21:26 how a0=1 ?
there is only one way to get a string of length 0
7:20 How does -2A2^n become -2^(n+1)An ?
2^n * 2 = 2^(n+1) was used and An was left unchanged
negative number the power of zero is negative one why you say 1 in the second question?
Or, you could just use the z-transform and inverse-z transform.
I didn't get why did we multiply with n
@@Limerain
If the root are identical like r 2,2
I LOVE YOU
No Homo.
love u too