Dynamical%20Systems%20in%20Linear%20Algebra%20and%20Differential%20Equations

1
Dynamical Systems in Linear Algebra and
Differential Equations

• Douglas B. Meade
• University of South Carolina
• E-mail meade_at_math.sc.edu
• URL http//www.math.sc.edu/meade/

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

3
Dynamical Systems Linear Algebra

• Basic Model x n1 A x n
• General Form of Solution xn ln
• Stability l lt 1

4
Dynamical Systems Differential Equations

• Basic Model x B x
• General Form of Solution x(t) elt
• Stability l lt 0

5
Dynamical Systems Connections between LA and DE

• x n1 A x n
• x B x
• B A - I
• lB lA - 1

6
Student Projects

• Initial Analysis of the Spotted Owl
• Eigenvalue Analysis of the Spotted Owl

7
Reference

• David C. Lay, Linear Algebra and Its
  Applications, Updated Second Edition, Addison
  Wesley Longman, 2000.
• URL http//www.laylinalgebra.com/
• Instructors Manuals MATALB, Maple,
  Mathematica, .