Discrete Mathematics - Vol 2 | 15. Solving Linear Homogeneous Recurrence Equations – Part II by Abraham | Learn Smarter
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15. Solving Linear Homogeneous Recurrence Equations – Part II

The lecture focused on solving linear homogeneous recurrence equations, particularly cases where characteristic roots may be repeated. It elaborated on techniques to derive general solutions for recurrence relations of degree n and discussed how these solutions change depending on the nature of the roots, specifically emphasizing the transition from distinct to repeated roots. The lecture provided examples illustrating the application of these concepts, including how to satisfy specific initial conditions.

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Sections

  • 15

    Solving Linear Homogeneous Recurrence Equations – Part Ii

    This section continues the exploration of linear homogeneous recurrence equations, focusing specifically on cases where the characteristic roots are repeated.

    Learning Practice

  • 15.1

    Recap Of Last Lecture

    This section summarizes key points from the previous lecture on solving linear homogeneous recurrence equations.

    Learning Practice

  • 15.2

    Case With Repeated Characteristic Roots

    This section discusses solving linear homogeneous recurrence equations in the context of repeated characteristic roots, explaining how the general form of solutions changes from cases of distinct roots.

    Learning Practice

  • 15.3

    General Form And Initial Conditions

    This section discusses the general structure for solving linear homogeneous recurrence equations and how to handle initial conditions.

    Learning Practice

  • 154

    Theorem Statement For Distinct Roots

    This section discusses the theorem related to linear homogeneous recurrence equations when the characteristic roots are distinct.

    Learning Practice

  • 15.5

    Example With Degree 2 Characteristic Equations

    This section covers the approach to solving linear homogeneous recurrence equations of degree 2 with repeated roots, illustrating the general form of the solution.

    Learning Practice

  • 15.6

    General Case For Degree K With Repeated Roots

    This section discusses how to solve linear homogeneous recurrence equations of degree k when the characteristic roots are repeated.

    Learning Practice

  • 15.7

    Theoretical General Form Of The Solution

    In this section, the focus is on deriving the general forms of solutions for linear homogeneous recurrence equations, specifically when characteristic roots are distinct or repeated.

    Learning Practice

  • 15.8

    Example Application Of General Formula

    This section focuses on solving linear homogeneous recurrence equations, particularly when the characteristic roots are repeated.

    Learning Practice

References

ch37.pdf

Class Notes

Memorization

What we have learnt

  • Linear homogeneous recurren...
  • The general form of the sol...
  • Initial conditions must be ...

Final Test

Revision Tests