Dynamical Systems in Linear Algebra and Differential Equations

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Presentation transcript:

Dynamical Systems in Linear Algebra and Differential Equations Douglas B. Meade University of South Carolina E-mail: meade@math.sc.edu URL: http://www.math.sc.edu/~meade/ 11/19/2018

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 11/19/2018

Dynamical Systems: Linear Algebra Basic Model: x n+1 = A x n General Form of Solution: xn = ln Stability: |l| < 1 11/19/2018

Dynamical Systems: Differential Equations Basic Model: x’= B x General Form of Solution: x(t) = elt Stability: |l| < 0 11/19/2018

Dynamical Systems: Connections between LA and DE x n+1 = A x n x’= B x B = A - I lB = lA - 1 11/19/2018

Student Projects Initial Analysis of the Spotted Owl Eigenvalue Analysis of the Spotted Owl 11/19/2018

Reference David C. Lay, Linear Algebra and Its Applications, Updated Second Edition, Addison Wesley Longman, 2000. URL: http://www.laylinalgebra.com/ Instructor’s Manuals: MATALB, Maple, Mathematica, …. 11/19/2018