Abstract

Citation

Researchers should cite this work as follows:

• Malagon, A. (2023). 2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling. SIMIODE, QUBES Educational Resources. doi:10.25334/5XF6-NE05

  BibTex | EndNote

Article Context

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

• Slide Deck containing all slides in video series – can be used for synchronous presentation in remote format, or as a basis to create your own videos for students.
• Modeling Activity Student Handout
• https://qubeshub.org/publications/3206/serve/1/15901?el=1&download=1
• Modeling Activity Teacher Version with Solutions

https://qubeshub.org/publications/3206/serve/1/15903?el=1&download=1

• 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