Abstract
In the preceding chapter, we saw that linear systems of differential equations were used to calculate the partial derivatives of the solutions of non-linear systems of differential equations taken as functions of the initial data and of the parameters. This is not the only example in which linear systems are used to study non-linear systems; one of the most frequently used techniques for studying the non-linear system
is that of decomposing fi into the sum of a linear and a non-linear part
using, for example, Taylor’s formula, and comparing the solutions of the linear system
with those of the original system. Other examples of this procedure will be treated in Chapters IV and V. It therefore seems useful to study the properties of the solutions of linear systems in greater depth.
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© 1984 Springer-Verlag New York Inc.
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Piccinini, L.C., Stampacchia, G., Vidossich, G. (1984). Linear Systems. In: Ordinary Differential Equations in Rn. Applied Mathematical Sciences, vol 39. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5188-0_2
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DOI: https://doi.org/10.1007/978-1-4612-5188-0_2
Publisher Name: Springer, New York, NY
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