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SMIS: A Stepwise Multiple Integration Solver Using a CAS

Author

Listed:
  • José Luis Galán-García

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

  • Pedro Rodríguez-Cielos

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

  • Yolanda Padilla-Domínguez

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

  • María Ángeles Galán-García

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

  • Iván Atencia

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

  • Pablo Rodríguez-Padilla

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

  • Gabriel Aguilera-Venegas

    (Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain
    These authors contributed equally to this work.)

Abstract

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to deal with this topic and (2) to be used in Math Education providing an important tool for helping with the teaching and learning process of this topic. SMIS can provide just the final solution or an optional stepwise solution (even including some theoretical comments). The optional stepwise solutions provided by SMIS are of great help for (2). Although SMIS has been developed in the specific CAS Derive , since the code is provided, it can be easily migrated to any CAS which deals with integrals and text management that allow us to display comments for intermediate steps.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2866-:d:676887
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    References listed on IDEAS

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    1. 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.
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