Difference Equations with Application Problems: Population Dynamics & Fitness Models

In this video, part of our linear algebra series, we dive deep into difference equations and their applications in modeling dynamical systems. Learn what a difference equation is, how it relates to discrete time intervals, and see it in action as we explore two real-world problems: population dynamics of frogs and fitness levels in individuals.

In the first example, we'll model how tadpoles mature into adult frogs and calculate population changes over time. In the second example, we'll use difference equations to understand how unfit, fit, and superfit individuals change over time.

Be sure to download the free guided notes (link below) to follow along and practice on your own. These notes include space to highlight key concepts and solve the example problems as we work through them.

*Link to Guided Notes*
Free downloadable pdf of guided notes that will help you follow along with the video and use later to review what you learned.

_Linear Equations in Linear Algebra:_

_Matrix Algebra:_

_Determinants_

_Vector Spaces_

_Eigenvalues and Eigenvectors_

_Orthogonality and Least Squares_

*Subscribe to My YouTube Channel*

*Visit the Understand The Math Website*
Find free guided notes, filled in guided notes for purchase, course outlines/playlists, and math merchandise.

*Connect on Social Media*

*Timestamps*
00:00 Introduction
01:00 Homogeneous Linear Systems
05:00 Solving a Homogeneous Linear System
07:30 Non-Homogeneous Linear Systems
10:30 Parametric Vector Form & Geometry
15:30 Simultaneous Systems & Augmented Matrices

*More About Understand The Math*
Understand The Math provides students and lifelong learners with access to free, straightforward, and engaging mathematics instruction. I’m Cheryl Hile, the founder of Understand The Math, and I’m passionate about ensuring that accurate and engaging mathematics instruction is available to everyone! I have a Ph.D. in Engineering Science and Applied Mathematics and have over 25 years of teaching experience at the university level. This channel provides videos that contain clear explanations, step-by-step problem solving strategies, and carefully worked out example problems. In the video descriptions, you'll find a link to free guided notes. Students can use these notes to highlight concepts and fill in answers to example problems while watching the videos, and later, they can review what they've learned.

#DifferenceEquations #LinearAlgebra #PopulationDynamics #FitnessModel #MathTutorial #UnderstandTheMath #DynamicalSystems #MatrixAlgebra #MathHelp #CollegeMath