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Students and Mathematica: Swirl Discoveries: A 2D Linear Differential Equations Investigation

Nathan Linger
Journal / Anthology

Mathematica in Education and Research
Year: 2000
Volume: 9
Issue: 3-4
Page range: 54-57

The coefficient matrix of 2-dimensional linear differential equation systems has complex eigenvalues and eigenvectors if and only if there are lines of attraction. The proof arose from and makes use of a graphical field plot representation of such systems. The use of Mathematica for both algebraic calculation and generation of these field plots allowed the proof to arise quite naturally.

*Mathematics > Calculus and Analysis > Differential Equations
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swirl.nb (211.2 KB) - Mathematica Notebook