SIMIODE

Geometric Behavior of Linear Systems Module Overview

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 to solve linear, homogeneous first order systems before beginning this unit.

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:

All videos are available by clicking on BoldFace Video and Number, but they are also available in Supportingt Docs for this General Resource for download.

• 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. (editable)
• Modeling Activity Student Handout Link (editable versions included)
• Modeling Activity Teacher Version with Solutions Link (editable versions included)
• 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 (editable)

Thanks to Kristin Burney, Virginia Wesleyan University, who provided the Mathematica images used in the presentation and gave valuable feedback on materials. 

Researchers should cite this work as follows:

• Audrey Malagon (2020), "2020-Malagon, Audrey - Remote Teaching Module - Geometry of Linear Systems," https://www.simiode.org/resources/7822.

  BibTex | EndNote

1. geometry
2. linear
3. module