The use of phase portraits to visualize and investigate isolated singular points of complex functions
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[1] University of Queensland
University of Queensland
Australia
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 50, Nº. 7, 2019, págs. 999-1010
- Idioma: inglés
- DOI: 10.1080/0020739x.2019.1656829
- Texto completo no disponible (Saber más ...)
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Resumen
Undergraduate students usually study Laurent series in a standard course of Complex Analysis. One of the major applications of Laurent series is the classification of isolated singular points of complex functions. Although students are able to find series representations of functions, they may struggle to understand the meaning of the behaviour of the function near isolated singularities. In this paper, I briefly describe the method of domain colouring to create enhanced phase portraits to visualize and study isolated singularities of complexfunctions. Ultimately this methodfor plotting complexfunctions might help to enhance students’ insight, in the spirit of learning by experimentation. By analysing the representations of singularities and the behaviour of the functions near their singularities, students can make conjectures and test them mathematically, which can help to create significant connections between visual representations, algebraic calculations and abstract mathematical concepts.
