Discrete Math II - 8.2.4 Non-Homogeneous Linear Recurrence Relations

Our final lesson (for a bit) on solving recurrence relations introduces us to non-homogeneous recurrence relations. This occurs when, in addition to using previous values in our sequence, we also use a function of n to determine subsequent values. You should already be familiar with solving homogeneous recurrence relations before watching this video.

Video Chapters:
Intro 0:00
What is a Non-Homogeneous Recurrence Relation 0:06
Guessing the Form of the Non-Homogeneous Recurrence Relation 1:53
Practice 1 F(x)=2n 4:20
Practice 2 F(x)=2^n 15:29
Up Next 21:40

This playlist uses Discrete Mathematics and Its Applications, Rosen 8e

Power Point slide decks to accompany the videos can be found here:

The entire playlist can be found here:

[arjunragu]

THANK YOU!! You are playing a huge part in my discrete mathematics journey! I may end up passing Discrete math after all!

[hubbadubchub]

Man, chapter 8 is a bit of a doozy!! Can't say thank you enough for these videos. I would be entirely lost if it wasn't for you.

[whatwedointhyshadows]

"Choose whatever variable makes your heartbeat faster."

[Haddy]

On duration 18:13, you have substituted an for Cn 2^n. Why tho? I didn't get it.

[alexnicolazzo]

After discovering your videos I went from bieng scared to pass descrete math with a C- to the real possibility of passing with a A

[miracleaugusto]

Hi thanks for such a great video, but i have small doubt. Like my equation is an=(3*an-1)-(2*an-2)+3( -1 and -2 are in subscript) by solving homogeneous part, i get A*2^n+B. For particular solution my guess function is C. If we substitute we get C=C+3. So here what is value of C as C=C+3 has infinite soln. I will be thankful if you could help me in this

[annevanderbijl]

I got the inhomogenous relation a_n = 6a_n-1 - 5a_n-2 + 1.
Unfortunately, guessing a^p_n = c doesn't seem to work.
Can you help me out?

[lw.lonewolf]

I'm barely passing, the paper's at 9 in the morning and here I am at 3am watching through your videos as fast as possible. I hope i pass :_:

[nobdagamer]

at 18:00 why n is added there from table n should not be there am i right ?

[nunu.g]

Omg thankyou so much you made it way easier to understand😊

[diyideas]

5:41 Didnt we write A(r)^n + B(n)(r)^n while solving the homogenous part in case we get a single root in the previous videos?

[samihanowshin]

If your vedio is more than 20 minute i will be more happy, Not matter what the duration is.. If It's for 1 hour then Also I will looking forward to such Quality Content ❤️

[sammartin]

what would your guess be if f(n) was of the form n * (r ^ n)?

[ceejay]

Your content defeinly belongs on Udaicy or EDX or something. I've only seen a bit of it but it's so good.

[chanhungnguyen]

can you explain more about why u implied that the coefficients in the equation:
-2n(c+1) + (-2d+3c) = 0 are equal to zero?? I'm rly confused bout this. Hope u'd tell me ...

[ksfaq]

Is there a video that u solved the first type witch is c?

[Brightest-tube]

thankyou i love you the course it is very nice again thankyou very much