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5-012-LinearSystemConjecture-TechniqueNarrative

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: discovery learning conjecture solution substitution

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Abstract

Resource Image Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student discovery.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

For our linear homogenous system of two differential equations we  conjecture a vector solution for X(t) which has the best of both worlds

(1) nice exponential form with no matrices in the exponent and

(2) vector status where we can see the pieces of the solution.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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