## Resources

Article or Presentation

## 2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling

Author(s): Audrey Malagon

Virginia Wesleyan University, Virginia Beach VA USA

Keywords: module linear systems digoxin Teaching Module

## Abstract

This module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students should be familiar with using eigenvalues.

## Citation

Researchers should cite this work as follows:

## Description

Prerequisites (Reviewed in the materials):

•      Converting a 2 x 2 linear homogenous system to matrix form

•      Finding eigenvalues and eigenvectors

•      Creating general solutions using eigenvalues and eigenvectors (real and complex)

Module Components:

• Video Series covering geometric properties of linear systems. This can be assigned to students in asynchronous or synchronous classes.
• Video 1: General review of how to convert 2 x 2 linear systems to matrix form and find eigenvalues
• Video 2: Geometric properties of systems with 2 distinct real eigenvalues
• Video 3: Geometric properties of systems with complex eigenvalues
• Video 4: Special cases (repeated and zero eigenvalues)
• Video 5: Trace Determinant Plane

• Modeling Activity Video Series
• Video 1: Introduction to the scenario, guidance through creating a diagram and the system of differential equations.
• Video 2: Overview of the rest of the project and instructions on how to use free online graphing software.

https://homepages.bluffton.edu/~nesterd/apps/slopefields.html

https://www.desmos.com/calculator

Modeling Activity Assessment Guide

## Authors

Author(s): Audrey Malagon

Virginia Wesleyan University, Virginia Beach VA USA