added small paragraph on singularities
This commit is contained in:
parent
b1cd3ef2de
commit
17ef8dc9c1
@ -194,7 +194,7 @@ We refer the interested reader to the excellent book of Moiseyev for a general o
|
||||
\titou{Discussion around the different types of singularities in complex analysis.
|
||||
At a singular point, a function and/or its derivatives becomes infinite or undefined (hence non analytic).
|
||||
One very common type of singularities (belonging to the family of isolated singularities) are poles where the function behaves $1/(\lambda - \lambda_c)^n$ where $n \in \mathbb{N}^*$ is the order of the pole.
|
||||
Another class of singularities are branch points resulting from a multi-valued function such as a square root or a logarithm function and usually implying the presence of so-called branch cuts where the function ``jumps'' from one value to another.
|
||||
Another class of singularities are branch points resulting from a multi-valued function such as a square root or a logarithm function and usually implying the presence of so-called branch cuts which are lines or curves where the function ``jumps'' from one value to another.
|
||||
Yet another family of singularities are formed by critical points which lie on the real axis, have more complicated functional forms and where the nature of the function undergoes a sudden transition.
|
||||
}
|
||||
|
||||
|
Loading…
Reference in New Issue
Block a user