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.

Highlights

  • A Computer Algebra System (CAS) is a computer software which deals with different mathematics topics

  • The two DERIVE files stepwise multiple integration solver (SMIS).mth and SMIS.dfw containing the library of developed programs and the tutorial of SMIS can be freely downloaded at https://acortar.link/SMIS

  • Depending on the use of Cartesian or polar coordinates, two different programs have been considered in SMIS

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Summary

Introduction

A Computer Algebra System (CAS) is a computer software which deals with different mathematics topics. The main objective of the present work is to develop the new stepwise multiple integration solver (SMIS) with the same aim as that of SFOPDES, that is, obtaining the final solution of a multiple integral computation and providing (optionally) all the intermediate steps needed to obtain the final solution This way, SMIS can be used to compute multiple integrals (needed in many Engineering applications) but it can be used as a tutorial in the teaching and learning process of the topics involving multiple integration. DERIVE can provide the rules used when computing an integral if the user presses the step by step button available in the Calculus menu This fact is very interesting but this stepwise solution defers from the one obtained with the programs developed in SMIS, since the user cannot obtain information on the theory involved or specific comments on intermediate steps. The integration rules of RUBI have been incorporated in other systems such as SYMJA (Symbolic Java [23]) and, partially, in SYMPY [24]

Description of SMIS
Global Variables
Double Integral in Cartesian Coordinates Syntax
Double Integral in Polar Coordinates Syntax
Triple Integral
Triple Integral in Cartesian Coordinates Syntax
Triple Integral in Cylindrical Coordinates
Triple Integral in Spherical Coordinates Syntax
Surface Integrals
Divergence Theorem
3.10. Green’s Theorem
The Use of SMIS in Mathematics Education
Conclusions and Future Work
Findings
Future Work
Full Text
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