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Abstract
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
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.
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