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Improving CAS capabilities: New rules for computing improper integrals

Author

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  • Galán-García, José L.
  • Aguilera-Venegas, Gabriel
  • Galán-García, María Á.
  • Rodríguez-Cielos, Pedro
  • Atencia-Mc.Killop, Iván

Abstract

Different Engineering applications require dealing with improper integral on unbounded domains (improper integrals of the first kind). The classical way for solving these integrals is by means of elementary Calculus (antiderivatives and limit computations) or using numerical approaches. In both situations different problems can arise. For example: the non-existence of antiderivative, the corresponding limit does not exist or integrals depending on parameters which complicate the use of numerical approaches. In order to solve this situation, Advanced Calculus techniques, such as Laplace or Fourier Transforms and the Residue Theorem can be applied. A brief review of the corresponding theoretical frame is included in this paper.

Suggested Citation

  • Galán-García, José L. & Aguilera-Venegas, Gabriel & Galán-García, María Á. & Rodríguez-Cielos, Pedro & Atencia-Mc.Killop, Iván, 2018. "Improving CAS capabilities: New rules for computing improper integrals," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 525-540.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:525-540
    DOI: 10.1016/j.amc.2016.12.024
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    References listed on IDEAS

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    1. Aguilera, Gabriel & Luis Galán, José & Madrid, Rafael & Martínez, Antonio Manuel & Padilla, Yolanda & Rodríguez, Pedro, 2010. "Automated generation of contrapuntal musical compositions using probabilistic logic in Derive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1200-1211.
    2. Roanes-Lozano, Eugenio & Galán-García, José Luis & Aguilera-Venegas, Gabriel, 2015. "A portable knowledge-based system for car breakdown evaluation," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 758-770.
    3. Aguilera, Gabriel & Galán, José Luis & García, José Manuel & Mérida, Enrique & Rodríguez, Pedro, 2014. "An accelerated-time simulation of car traffic on a motorway using a CAS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 21-30.
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    Cited by:

    1. José Luis Galán-García & Pedro Rodríguez-Cielos & Yolanda Padilla-Domínguez & María Ángeles Galán-García & Iván Atencia & Pablo Rodríguez-Padilla & Gabriel Aguilera-Venegas, 2021. "SMIS: A Stepwise Multiple Integration Solver Using a CAS," Mathematics, MDPI, vol. 9(22), pages 1-32, November.
    2. Valentina Petrova Todorova-Lazarova & Todor Dimitrov Todorov, 2024. "Some Aspects of Teaching Improper Integrals in an Electronic Environment," Mathematics, MDPI, vol. 12(17), pages 1-13, August.

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