simple pole: meaning, definition, pronunciation and examples
C2Technical/Academic
Quick answer
What does “simple pole” mean?
In complex analysis, a type of isolated singularity of a complex function where the function behaves like 1/(z-a) near the point a, with the function's Laurent series having a finite number of negative-power terms.
Audio
Pronunciation
Definition
Meaning and Definition
In complex analysis, a type of isolated singularity of a complex function where the function behaves like 1/(z-a) near the point a, with the function's Laurent series having a finite number of negative-power terms.
A pole of order one; the simplest type of pole where the function goes to infinity linearly as the variable approaches the singularity. In broader technical contexts, it can refer to a first-order singularity in various mathematical or physical systems.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling conventions follow standard British/American rules for the word 'simple'.
Connotations
Identical technical connotations in both varieties.
Frequency
Equally low frequency and confined to highly technical discourse in both varieties.
Grammar
How to Use “simple pole” in a Sentence
The function f(z) has a simple pole at z = a.A simple pole of order one occurs at the origin.Vocabulary
Collocations
Examples
Examples of “simple pole” in a Sentence
adjective
British English
- The simple-pole behaviour was evident from the graph.
American English
- The simple-pole behavior was evident from the graph.
Usage
Meaning in Context
Business
Not used.
Academic
Used in advanced mathematics, physics, and engineering lectures and papers on complex analysis.
Everyday
Not used.
Technical
Core term in complex analysis, signal processing, and control theory when describing system transfer functions.
Vocabulary
Synonyms of “simple pole”
Neutral
Weak
Vocabulary
Antonyms of “simple pole”
Watch out
Common Mistakes When Using “simple pole”
- Using 'simple pole' in non-technical contexts.
- Confusing it with a 'double pole' or higher-order pole.
- Incorrectly assuming 'simple' implies the concept is easy to understand.
FAQ
Frequently Asked Questions
Yes, these terms are completely synonymous in complex analysis.
No, a simple pole is an isolated singularity that is not removable. The function inherently goes to infinity at that point.
Primarily in university-level mathematics (complex analysis), theoretical physics, and certain branches of engineering like control systems or electrical engineering.
Not exactly. It means it is of the lowest order (order one), which often makes calculations like finding residues more straightforward compared to higher-order poles, but the concept itself is advanced.
Simple pole is usually technical/academic in register.
Simple pole: in British English it is pronounced /ˌsɪmpl ˈpəʊl/, and in American English it is pronounced /ˌsɪmpl ˈpoʊl/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a simple pole as a 'first offence' singularity – it misbehaves (goes to infinity) but in the most straightforward, predictable way (order one).
Conceptual Metaphor
A singularity with a single, clear 'charge' or 'weight' (the residue).
Practice
Quiz
What is the defining characteristic of a simple pole?