Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter
7: Systems of First Order Linear Equations
Definitions:
•
Systems of ODE's
•
Linear vs. Nonlinear Systems
•
Solution
•
Preypredator system
•
Homogenous and Nonhomogeneous Systems Matrix,
•
Transpose, Conjugate, Adjoint, Determinant Scalar
•
(Inner) Product, Orthogonal
•
Nonsingular (Invertible) and Singular (Noninvertible)
•
Row Reduction (Gaussian Elimination)
•
Linear Systems, Homogeneous, Nonhomogeneous
•
Augmented Matrix
•
Linear Dependence and Independence
•
Eigenvalues, Eigenvectors, Generalized Eigenvectors
•
The matrix exp(
At
)
•
Normalization
•
Multiplicity m, Simple Multiplicity (m = 1)
•
Self Adjoint (Hermitian)
•
General Solution, Fundamental Set of Solutions
•
Phase Plane, Phase Portrait
•
Generalized eigenvector
•
Node, Saddle Point, Spiral Point, Improper Node
•
Fundamental Matrix
•
Similarity Transformation, Diagonalizable
Theorems:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 DorothyWallace
 Differential Equations, Linear Algebra, Linear Equations, Equations, Linear Systems, Elementary Differential Equations, Chapter Review Sheets

Click to edit the document details