12The Nonlinear Theory
The nature of a nonlinear problem
Examples of nonlinear problems
Critical points
Stability
Linear systems
Lyapunov's direct method
Nonlinear systems
Nonlinear mechanics
Periodic solutions
Poincaré–Bendixson theory
Both the historical and the textbook development of the subject matter of this book might lead one to think that ordinary differential equations is primarily about linear equations. Historically speaking this has certainly been the case.
It is definitely true that the linear equations are the most tractable, they are the ones that we understand best, and they are the ones for which there is the most complete theory. But in fact the world is largely nonlinear. We have traditionally ...
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