1. Dynamical Systems in Linear Algebra and Differential Equations
Douglas B. Meade
University of South Carolina
URL:
11/19/2018

2. Overview
Dynamical systems are appropriate for both linear algebra and differential equations.
Eigenvalues are an essential tool in the qualitative analysis of dynamical systems viz., stability.
Student Projects: Spotted Owl
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3. Dynamical Systems: Linear Algebra
Basic Model: x n+1 = A x n
General Form of Solution: xn = ln
Stability: |l| < 1
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4. Dynamical Systems: Differential Equations
Basic Model: x’= B x
General Form of Solution: x(t) = elt
Stability: |l| < 0
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5. Dynamical Systems: Connections between LA and DE
x n+1 = A x n
x’= B x
B = A - I
lB = lA - 1
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6. Student Projects Initial Analysis of the Spotted Owl
Eigenvalue Analysis of the Spotted Owl
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7. Reference
David C. Lay, Linear Algebra and Its Applications, Updated Second Edition, Addison Wesley Longman,
URL:
Instructor’s Manuals: MATALB, Maple, Mathematica, ….
11/19/2018