Abstract
Differential equations are as varied as the phenomena of nature described by them.
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Notes
- 1.
At surface level, \(g=9.81\,\mathrm{m/s}^2\).
- 2.
Numerical methods for the solution of differential equations are discussed, for instance, in Griffiths and Higham [GH].
- 3.
With the stipulation \(r/N:=+\infty \) when \(N=0\).
- 4.
For instance, with a norm coming from a Riemannian metric.
- 5.
We will always work in spaces whose topology is metrizable, so we understand
$$\limsup _{x\rightarrow x_0}f(x)\quad \text{ as }\quad \lim _{\varepsilon \searrow 0} \sup \big \{f(x)\mid x\in U_\varepsilon (x_0)\setminus \{x_0\}\big \}.$$In general such a function is lower semicontinuous exactly if its epigraph is closed.
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Knauf, A. (2018). Ordinary Differential Equations. In: Mathematical Physics: Classical Mechanics. UNITEXT(), vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55774-7_3
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DOI: https://doi.org/10.1007/978-3-662-55774-7_3
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