This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 5.4 (Systems of Linear Differential Equation); 9.5 Eigenvalues and Eigenvectors April 21, 2009 2 2 Systems of Linear Differential Equations Todays Session Problems to work on, but will not be posted on webassign : 9.5: 2, 4, 9, 11, 12, 18, 22, 26. Handin for Nov 25: 9.5 # 31. Bring your clickers on Thursday! A Summary of This Session: (1) More about eigenvalues and eigenvectors of a 2 2 matrix. (2) 2 2 systems of differential equations (not necessarily linear) (3) Phaseplane method (types of nodes) 2 2 Systems of Linear Differential Equations Critical points, critical point set, equilibrium point(s) Example 1: Consider the system: x = x + 3 y = 2 y + 2 Find the critical point(s), eigenvalues and eigenvectors, and describe completely the solution set. To find the critical points, one needs to solve, simultaneously, x = 0 y = 0 This means: x + 3 = 0 2 y + 2 = 0 So the critical point is (3,1). 2 2 Systems of Linear Differential Equations Example 1: Case of a Stable Node To find the eigenvalues, we first put the system in the form v = A v + v Where v = parenleftbigg x y parenrightbigg , A = parenleftbigg 1 2 parenrightbigg...
View
Full
Document
 Spring '08
 INDIK
 Differential Equations, Equations

Click to edit the document details