Discrete Mathematics - Vol 2 | 14. Solving Linear Homogenous Recurrence Equations – Part I by Abraham | Learn Smarter
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14. Solving Linear Homogenous Recurrence Equations – Part I

The lecture explores solving linear homogenous recurrence equations, particularly focusing on cases with non-repeated characteristic roots. It presents a systematic method for constructing characteristic equations and deriving general solutions based on the given degree of the recurrence. The importance of initial conditions in determining unique sequences is emphasized, alongside an illustrative example involving the Fibonacci sequence.

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Sections

  • 14

    Solving Linear Homogenous Recurrence Equations – Part I

    This section discusses the solving of linear homogeneous recurrence equations, specifically focusing on the case with non-repeated characteristic roots.

    Learning Practice

  • 14.1

    Recap Of Previous Lecture

    This section recaps the essential concepts introduced in the previous lecture regarding solving linear homogeneous recurrence equations.

    Learning Practice

  • 14.2

    Definition Of Linear Homogeneous Recurrence Equations

    This section introduces linear homogeneous recurrence equations, emphasizing their formulation and methods for finding solutions.

    Learning Practice

  • 14.3

    General Method For Solving Recurrence Equations

    This section discusses the general method for solving linear homogeneous recurrence equations, particularly focusing on equations with non-repeated characteristic roots.

    Learning Practice

  • 14.4

    Demonstration With Degree 2 Recurrence Equations

    This section explores solving linear homogeneous recurrence equations of degree 2, detailing methods to derive closed-form solutions and understanding characteristic roots.

    Learning Practice

  • 14.5

    Characterization Of Sequences

    This section discusses the principles and methods for characterizing and solving linear homogeneous recurrence equations, particularly those with non-repeated characteristic roots.

    Learning Practice

  • 14.6

    Theorem Statement

    The theorem provides the general solution form of linear homogeneous recurrence equations with distinct roots.

    Learning Practice

  • 14.7

    Proof Of Theorem - Part 1

    This section introduces the proof for solving linear homogeneous recurrence equations with distinct characteristic roots.

    Learning Practice

  • 14.8

    Proof Of Theorem - Part 2

    This section elaborates on the proof of a theorem related to linear homogeneous recurrence equations, specifically focusing on the case with distinct characteristic roots.

    Learning Practice

  • 14.9

    Extension To Degree K Linear Homogeneous Recurrence Equations

    This section discusses the methodology for solving linear homogeneous recurrence equations of degree k, particularly focusing on those with distinct characteristic roots.

    Learning Practice

References

ch36.pdf

Class Notes

Memorization

What we have learnt

  • Linear homogenous recurrenc...
  • When roots are distinct, th...
  • Initial conditions are cruc...

Final Test

Revision Tests