Solving Difference Equations and Recurrence Relations

A Complete Video Tutorial

All Levels 3.4(4 Ratings) 1,505 Students enrolled
Created by Yarpiz Team Last updated 12/2019 English ["English [Auto-generated]"]
What will i learn?
  • General form of ordinary linear difference equations
  • How to solve homogeneous linear difference equations
  • How to solve non-homogeneous linear difference equations
  • Solving difference equations with repeated roots in characteristic equation

Curriculum for this course
8 Lectures 00:35:45
Solving Difference Equations
8 Lectures 00:35:45
  • Introduction 00:02:49
  • Solving a General Second-Order Difference Equation 00:03:52
  • The Fibonacci Series as a Difference Equation 00:04:46
  • More on Fibonacci Series and Golden Ratio 00:04:30
  • General Form of the Solution for a Difference Equation 00:02:07
  • Repeated Roots in Characteristic Equation 00:03:26
  • How to Solve Non-Homogeneous Difference Equations 00:08:00
  • Non-Homogeneous Difference Equations with Repeated Roots 00:06:15
Requirements
  • Basic Mathematics
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Description

Difference Equations , aka. Recurrence Relations, are very similar to differential equations, but unlikely, they are defined in discrete domains (e.g. discrete time or space). In this video tutorial, the general form of linear difference equations and recurrence relations is discussed and solution approach, using eigenfunctions and eigenvalues is represented. Some examples, including Fibonacci Series, are investigated in the video tutorial, as well. The case of multiple (non-distinct) roots of characteristic equation is also considered. Finally, the non-homogeneous difference equations are discussed, by providing the concept of general and particular solutions.

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About the instructor
  • 16 Students
  • 6 Courses
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