 Computing integrals over polynomially defined regions and their boundaries in 2 and 3 dimensionsMichael J. Wester, Yuzita Yaacob and Stanly Steinberg Mathematics and Computers in Simulation (MATCOM), 2011, vol. 82, issue 1, 79-101 Abstract: We use the cylindrical algebraic decomposition algorithms implemented in Mathematica to produce procedures to analytically compute integrals over polynomially defined regions and their boundaries in two and three dimensions. Using these results, we can implement the divergence theorem in three dimensions or the Green's theorems in two dimensions. These theorems are of central importance in the applications of multidimensional integration. They also provide a strong correctness test for the implementation of our results in a computer algebra system. The resulting software can solve many of the two and some of the three dimensional integration problems in vector calculus textbooks. The three dimensional results are being extended. The results in this paper are being included in an automated student assistant for vector calculus. Keywords: Area integral; Line integral; Volume integral; Surface integral; Iterated integrals; Cylindrical algebraic decomposition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2011:i:1:p:79-101 DOI: 10.1016/j.matcom.2011.06.003 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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