Lectures related to Recurrence relation

Counting with Recurrence Relations: Summary

Explores counting with recurrence relations, linear recurrence relations, generating functions, and counting principles.

Discrete Systems: Relations, Linear Dynamics, and Operators

Covers discrete systems, linear dynamics, causality, impulse response, convolution, and operators' effects.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Difference Equations: Roots and Solutions

Explores characteristic polynomials, stability conditions, homogeneous solutions, and transfer functions in difference equations.

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Sequences: Arithmetic and Geometric Progressions

Covers arithmetic and geometric progressions, strings, and recurrence relations.

Sequences: Relations, Summation, Strings

Covers arithmetic and geometric progressions, strings, and recurrence relations in sequences.

Discrete Systems Theory

Covers difference equations, dynamic systems, linearity, and impulse response in discrete systems.

Difference Equations

Covers the concept of difference equations and properties of causal vs. stable systems.

Geometric Sequences: Recurrence System

Covers geometric sequences and recurrence systems to find sequence terms and patterns.

Counting with Recurrence Relations: Fibonacci Sequence and Bit Strings

Covers the definition of recurrence relations and their application in counting problems.

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Z-Transform Properties

Covers the transfer function of composed LTI systems, difference equations, and Z-Transform properties.

Frobenius Method: Illustration around an Ordinary Point

Covers the Frobenius method for solving ODEs around an ordinary point.

Linear Recurrence Relations: Solving Techniques

Explores linear homogeneous recurrence relations, solving techniques, characteristic equations, and examples like Fibonacci numbers.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Signals & Systems II: Roots, Equations, and Impulse Responses

Explores roots verification, stability, reproduction modeling, Z transform, and LTI systems realization.

Difference Equations and Controllers

Covers linear difference equations, controllers, discretization, and approximation techniques.

Signals & Systems II: Difference Equations and Operators

Covers difference equations, z-transform method, system equivalence, and stability criteria.

Differential and Difference Equations

Explores differential and difference equations for causal LTI systems using examples of RC circuits and vehicle motion.