RT Conference Proceedings
T1 Teaching the residue theorem and its applications with a CAS
A1 Galán-García, José Luis
A1 Aguilera-Venegas, Gabriel
A1 Rodríguez-Cielos, Pedro
A1 Padilla-Domínguez, Yolanda Carmen
A1 Galán-García, María Ángeles
AB The residue theorem is one of the most interesting result in Complex Analysis which allowsnot only computations in C, the Field of Complex Numbers, but also provides many applicationsin the Field of Real Numbers R.In this talk we present the library ResidueApplications, that was initially developed inDERIVE since Engineering students in the University of Málaga are still using this softwarein computer lectures. However, we are migrating this library to PYTHON using the symbolicmathematics library SYMPY. This way it will be also possible to use this package in otherCAS as SAGEMATH.The main goals of the ResidueApplications library are not only to provide some importantapplications of the Residue theorem but also to use it as a pedagogical tool for Engineeringstudents.ResidueApplications can be used as a tutorial in the teaching and learning process ofthis topic since it provides the results step by step allowing the students to check their computationswhen they solve an exercise. When developing this package, we were not interestingonly in the computations of residues and their applications (which can be easily done usingstandards functions in different CAS) but mainly on its pedagogical use. In addition ofthe step by step facility, using this library, the students also can develop their own programsto deal with different applications. This way, the student are the protagonist of their selflearningprocess. For example, If the students develop a program to compute the residues ofa function, they will be better prepared to understand this topic.The programs developed in this tutorial can be grouped in the following blocks:1. Compute of residues.2. Compute of complex integrals using the residue theorem.3. Applications of the residue theorem to compute integrals in R:(a) Trigonometric integrals.(b) Improper integrals.
YR 2019
FD 2019-07-25
LK https://hdl.handle.net/10630/18148
UL https://hdl.handle.net/10630/18148
LA eng
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026