Abstract
Differential equations play a vital role in all fields of the natural and technical sciences, and increasingly also in economics and ecology. They describe deterministic processes or models thereof. They are equations in some unknown function of one or several variables such that the unknown function as well as its derivatives may occur.
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Notes
- 1.
Partial differential equations are differential equations for functions of several variables. For instance, the one-dimensional wave equation for the unknown function u(x, t) with x = position and t = time is \(\frac{\partial ^2u }{\partial t^2}= c^2 \frac{\partial ^2u }{\partial x^2}\).
- 2.
A general discussion follows  in Exercise 66 of Chap. 3.
- 3.
The notion of semi-stability is also used for limit cycles of solutions. In the interior and exterior of a limit cycle the solutions behave entirely differently: they are either attracted or repelled by the limit cycle.
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Fässler, A. (2019). First Order Differential Equations. In: Fast Track to Differential Equations. Springer, Cham. https://doi.org/10.1007/978-3-030-23291-7_2
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DOI: https://doi.org/10.1007/978-3-030-23291-7_2
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