Abstract
The book begins by a quick review of elementary properties about analytic and meromorphic functions, differential and difference equations, and differential forms. This part is not intended to explain concepts in depth; it indicates how much it is assumed about the background of the reader, and also serves to fix notation. After this review, the Cauchy–Kovalevskaya and the Frobenius theorems are discussed with some details. The last section of the chapter defines semi-simple, normal and nilpotent square matrices, and gives some first properties of them; many other properties that belong to the linear algebra field are actually reported in the second chapter, since there they can be explained or proven with reference to the central topics in this book.
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