Ebook: Matematiska metoder inom elläran

Whether one likes it or not, it happens to be the case that the theory of differential equations plays a fundamental role in many fields of application. Unfortunately, it is also a fact that, from a mathematical point of view, the theory of differential equations is very difficult and largely not yet understood (especially in the case of partial differential equations).

A course in differential equations is therefore very desirable from the point of view of application, but mathematically it cannot clear up more than a small part of all the existing question marks.

In this compendium, the authors have chosen to start by studying Picard's theorem, which states that under very moderate regularity conditions, ordinary differential equations are always locally solvable. The fact that differential equations in general do not have global solutions is easily seen from examples. But since applications are mostly interested in global solutions, it may be of interest to look at some special types of differential equations that are globally solvable.