2
VIII – Cauchy Theory
Learning to use basic ideas is, therefore, much better than learning a
multitude of general theorems, albeit ingenious and deep, unless, of course,
the aim is to specialize in general theory.
Cauchy theory (it would be much better to say : Cauchy and Weierstrass)
has been and continues to be the subject of many accounts merely differing
from each other on detailed points of presentation or style; not seeing the
need to reproduce them an umpteenth time, I have tried, whenever possible, not to follow them, in particular regarding homotopy. As will be seen
in the next chapter, apart from the residue theorem, another easy consequence, Cauchy’s method falls within the much more general framework of
multivariate differential forms.
VIII – Cauchy Theory
Learning to use basic ideas is, therefore, much better than learning a
multitude of general theorems, albeit ingenious and deep, unless, of course,
the aim is to specialize in general theory.
Cauchy theory (it would be much better to say : Cauchy and Weierstrass)
has been and continues to be the subject of many accounts merely differing
from each other on detailed points of presentation or style; not seeing the
need to reproduce them an umpteenth time, I have tried, whenever possible, not to follow them, in particular regarding homotopy. As will be seen
in the next chapter, apart from the residue theorem, another easy consequence, Cauchy’s method falls within the much more general framework of
multivariate differential forms.