Recurrence Relations

Definition and Examples

Initial Conditions

Order of Recurrence Relations

Modeling Problems with Recurrences

Tower of Hanoi

Fibonacci Numbers

Catalan Numbers

Tribonacci Numbers

Definition and Structure

First-Order Relations

Second-Order Relations

The Characteristic Equation

Distinct Roots Case

Repeated Roots Case

Complex Roots Case

General Solutions

Definition and Structure

Homogeneous and Particular Solutions

Method of Undetermined Coefficients

Variation of Parameters

Superposition Principle

Substitution Methods

Generating Function Approach

Matrix Methods