# ch07 - Chapter Review Sheets for Elementary Differential...

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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 Prey-predator 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:

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ch07 - Chapter Review Sheets for Elementary Differential...

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