Linear ODE Systems — Topic Summaries
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Ordinary Differential Equations 20 | Matrix Exponential
Solving a homogeneous autonomous linear system of differential equations reduces to computing a single object: the matrix exponential. For systems of...
Ordinary Differential Equations 19 | Solution Space
For systems of linear differential equations, the solution set has a rigid structure: in the homogeneous case, all solutions form an n-dimensional...
Ordinary Differential Equations 21 | Solution Set of Linear ODEs
A linear system of ordinary differential equations with a forcing term has a solution set that can be built from the homogeneous solutions plus just...
Ordinary Differential Equations 22 | Properties of the Matrix Exponential
Matrix exponentials turn linear systems of ordinary differential equations into an explicit solution formula: once a square matrix A is given, the...