SMIS: A Stepwise Multiple Integration Solver Using a CAS
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/22/2866 |
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| author | José Luis Galán-García Pedro Rodríguez-Cielos Yolanda Padilla-Domínguez María Ángeles Galán-García Iván Atencia Pablo Rodríguez-Padilla Gabriel Aguilera-Venegas |
| author_facet | José Luis Galán-García Pedro Rodríguez-Cielos Yolanda Padilla-Domínguez María Ángeles Galán-García Iván Atencia Pablo Rodríguez-Padilla Gabriel Aguilera-Venegas |
| author_sort | José Luis Galán-García |
| collection | DOAJ |
| description | 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 <span style="font-variant: small-caps;">Derive</span>, 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. |
| first_indexed | 2024-03-10T05:18:53Z |
| format | Article |
| id | doaj.art-817eb94d704d4789a6bd5f9b354f2695 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:18:53Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-817eb94d704d4789a6bd5f9b354f26952023-11-23T00:14:14ZengMDPI AGMathematics2227-73902021-11-01922286610.3390/math9222866SMIS: A Stepwise Multiple Integration Solver Using a CASJosé Luis Galán-García0Pedro Rodríguez-Cielos1Yolanda Padilla-Domínguez2María Ángeles Galán-García3Iván Atencia4Pablo Rodríguez-Padilla5Gabriel Aguilera-Venegas6Department of Applied Mathematics, University of Málaga, 29071 Málaga, SpainDepartment of Applied Mathematics, University of Málaga, 29071 Málaga, SpainDepartment of Applied Mathematics, University of Málaga, 29071 Málaga, SpainDepartment of Applied Mathematics, University of Málaga, 29071 Málaga, SpainDepartment of Applied Mathematics, University of Málaga, 29071 Málaga, SpainDepartment of Applied Mathematics, University of Málaga, 29071 Málaga, SpainDepartment of Applied Mathematics, University of Málaga, 29071 Málaga, SpainMultiple 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 <span style="font-variant: small-caps;">Derive</span>, 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.https://www.mdpi.com/2227-7390/9/22/2866computer algebra systemsmultiple integrationadvanced calculusmathematical programmingmathematical education |
| spellingShingle | José Luis Galán-García Pedro Rodríguez-Cielos Yolanda Padilla-Domínguez María Ángeles Galán-García Iván Atencia Pablo Rodríguez-Padilla Gabriel Aguilera-Venegas SMIS: A Stepwise Multiple Integration Solver Using a CAS Mathematics computer algebra systems multiple integration advanced calculus mathematical programming mathematical education |
| title | SMIS: A Stepwise Multiple Integration Solver Using a CAS |
| title_full | SMIS: A Stepwise Multiple Integration Solver Using a CAS |
| title_fullStr | SMIS: A Stepwise Multiple Integration Solver Using a CAS |
| title_full_unstemmed | SMIS: A Stepwise Multiple Integration Solver Using a CAS |
| title_short | SMIS: A Stepwise Multiple Integration Solver Using a CAS |
| title_sort | smis a stepwise multiple integration solver using a cas |
| topic | computer algebra systems multiple integration advanced calculus mathematical programming mathematical education |
| url | https://www.mdpi.com/2227-7390/9/22/2866 |
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