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4 cards from this section. Quick, good the night before a test.
What is the matrix form of a first-order ODE?
Recall how we represent systems in matrix notation.
What does e^(At) represent?
Think about how we use matrix exponentiation in differential equations.
What representation can be used to express a system of ODEs?
Think about how we express linear transformations.
True or False: The solution x(t) = e^(At)x(0) uses the inverse of matrix A.
Recall what e^(At) signifies in solving ODEs.
Consider a 2x2 matrix A with eigenvalues λ1=2 and λ2=-1. Analyze the long-term behavior of a system described by dx/dt = Ax.
Use the properties of eigenvalues to predict system behavior.
Given a matrix A that you can diagonalize, find the matrix exponential e^(At) when t=1. Start by finding its eigenvalues and eigenvectors.
Remember the diagonalization steps we discussed.
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