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Discrete Math II - 8.4.7 Solve Recurrence Relations with Generating Functions
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We will utilize everything we have learned in the previous 6 videos to learn how to solve recurrence relations using generating functions. This is a longer video, but there is a LOT of prior knowledge you will be tapping into. We take our time through one example involving partial fractions and solving a system of 3 equations. We end with creating the generating function from a recurrence relation that we previously solved for explicitly.
Video Chapters:
Intro 0:00
Helpful Table 0:15
Creating Equations from Your Recurrence Relation 0:24
Creating Summations from Addition of Recurrence Relations 1:26
Substituting the Power Series G(x) 4:13
The Generating Function G(x) 8:44
Write the Closed-Form Expression of the Generating Function 12:47
Solve a System of 3 Equations 17:09
Create the Explicit Function from the Generating Function 22:00
Checking Your Work 24:16
Practice for Creating a Closed-Form GenFun from Recur.Rel 25:01
Up Next 34:32
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:
Video Chapters:
Intro 0:00
Helpful Table 0:15
Creating Equations from Your Recurrence Relation 0:24
Creating Summations from Addition of Recurrence Relations 1:26
Substituting the Power Series G(x) 4:13
The Generating Function G(x) 8:44
Write the Closed-Form Expression of the Generating Function 12:47
Solve a System of 3 Equations 17:09
Create the Explicit Function from the Generating Function 22:00
Checking Your Work 24:16
Practice for Creating a Closed-Form GenFun from Recur.Rel 25:01
Up Next 34:32
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:
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